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Ukrainian officials said one person was killed and four injured after missiles struck a district near Kyiv's center. Meanwhile, G7 leaders are meeting in Germany.
This article was last updated at 20:31 UTC/GMT
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Russian Federation Council speaker Valentina Matvienko said that Russia is ready to negotiate only if Kyiv accepts Moscow's conditions.
The Federation Council is the upper house of Russia's parliament.
"If the West wanted to, it would sit Kyiv down at the negotiating table and force them to reach peace agreements," Matvienko said in an interview with the STV broadcaster.
"These are conditions that are stated for the purpose of a special military operation, and, of course, Russia will not negotiate on any other terms, because it was Ukraine that crossed the red line," she said.
Matvienko added that the West and NATO are "at war with Russia" via the proxy of Ukraine.
US Secretary of State Antony Blinken told CNN that Western sanctions are having "a profound impact" on Russia.
"Even as (Russia) gets oil revenues with higher prices it's unable to spend them because of the export controls," Blinken said in an interview at the G7 summit in Germany.
Russia can no longer "acquire what it needs to modernize its defense sector, to modernize its technology, to modernize its energy exploration, which means that over time each of these areas is going to go in decline," he added.
Blinken said the Russian economy is likely to shrink by up to 15% next year.
He added that the G-7 and NATO "will continue to do collectively everything we can to make sure that the Ukrainians have what they need in their hands to repel the Russian aggression."
US President Joe Biden has told G7 leaders gathered in Germany that the West must remain unified in its response to Russia's invasion of Ukraine.
"We have to stay together," he said in front of German Chancellor Olaf Scholz, the host of the three-day summit in the Bavarian Alps.
Russian President Vladimir Putin had been hoping "that somehow NATO and the G7 would splinter," Biden said. "But we haven't and we're not going to."
Scholz said "Putin never expected" Western unity, but added that each G7 member "needs to share responsibility" for facing the mounting challenges the war presents.
Ukrainian President Volodymyr Zelenskyy is set to call for more sanctions on Moscow and more heavy weapons for Kyiv when he joins the meeting via video link on Monday.
Around 250 more people have been evacuated from the Azot chemical factory in Sieverodonetsk after Ukraine relinquished control of the city, pro-Russian separatists said.
Some 200 civilians, including young children, were helped to leave the plant a day earlier, according to Rodion Miroschnikon, the Luhansk separatist representative in Moscow. It was unclear where the evacuees have been moved to.
The Ukrainian military governor of Luhansk had said there were 568 civilians sheltering in the air raid shelters set up in the plant before troops withdrew.
Ukrainian forces have attacked an oil platform in the Black Sea owned by a Crimean oil and gas company, Tass news agency reported, citing local officials.
It was the second strike on the rig in a week. Last Monday, three people were wounded and seven were reported missing in a Ukrainian strike, officials said.
The oil rig was seized by Russian-backed officials in 2014 from Ukraine's national gas operator Naftogaz when Moscow annexed the Crimean peninsula.
The platform's current operator Chernomorneftegaz is under US and EU sanctions.
Russia has denied as "fake" reports that it hit a residential area of Kyiv, insisting that its air strikes had struck a weapons factory.
The Artyom factory "was the target, as military infrastructure" the Russian Defense Ministry said, adding that it had already been targeted in April.
The ministry blamed a Ukrainian air defense missile for the damage to a nearby residential building.
It was not immediately possible to verify the claims.
Kyiv mayor Vitali Klitschko said Russian strikes hit the Shevchenkivsky district just after dawn on Sunday, damaging an apartment building and a kindergarten.
One person was killed and at least four others were wounded.
France has urged the world's oil producers to limit the price of oil to help squeeze the Russian economy.
A source in President Emmanuel Macron's office told Agence France-Presse that Paris backs a US proposal for a maximum oil price, but said that "it would be much more powerful if it came from the producing countries."
The source said it would be "necessary to get into a discussion with OPEC+ and with the world's oil producers," referring to the 23-country oil cartel.
Washington's suggestion of a price cap decided by consuming countries is due to be discussed by G7 leaders meeting in the Bavarian Alps.
Germany thinks the measure would be too difficult to put in place.
US President Joe Biden has praised the German government for its recent decision to boost defense spending by €100 billion ($106 billion).
"The president welcomed Germany's historic commitment to significantly boost defense spending and meet its NATO commitments, which will strengthen the alliance's long-term deterrence and defense posture," the White House said after Biden held one-on-one talks with Chancellor Olaf Scholz on the sidelines of the G7 summit in Bavaria.
"The leaders underlined their commitment to Ukraine's sovereignty and territorial integrity, as well as their continued provision of military, economic, humanitarian, and diplomatic support to help Ukraine defend its democracy against Russian aggression," the statement added.
Days after Russian troops entered Ukraine in late February, Scholz announced the massive spending commitment, which he said would help Germany meet NATO's target of spending 2% of GDP on defense.
The €100 billion commitment comes on top of this year's record defense budget of €50.4 billion and will be spent over the next five years.
Andriy Yermak, chief of staff to Ukrainian President Zelenksyy, said that the latest Russian strikes on Kyiv make clear that international sanctions on Russia should be more aggressive.
"The sanctions should be more aggressive. An embargo on gold exports is good, but a gas embargo is needed in the new EU sanctions package," Yermak said.
Yermak was referring to the decision taken by four countries at the G7 this morning to ban imports of Russian gold to further economically isolate Russia for its war in Ukraine.
Ukrainian Foreign Minister Dmytro Kuleba also called for more sanctions against Russia after Sunday's strikes.
"This seven-year-old Ukrainian kid was sleeping peacefully in Kyiv until a Russian cruise missile blasted her home," he wrote on Twitter, referring to a girl that was rescued from the rubble after the explosion in a residential building.
The EU adopted the sixth package of sanctions on Russia earlier this June and imposed a partial embargo on Russian oil. But, the bloc has not placed sanctions on Russian gas yet.
Russia's Defense Ministry said Russian forces struck three Ukrainian military training centers in northern and western Ukraine.
Strikes were carried out with "high-precision weapons of Russia's aerospace forces and Kalibr missiles," the ministry's statement read.
Russian news agencies said the military centers were located in the northern Chernihiv, the northwestern Zhytomyr and the western Lviv regions of Ukraine.
The center in Lviv was around 19 miles (30 kilometers) from the border with Poland, a NATO member.
NATO leaders are due to gather in Madrid, Spain, for their annual summit on June 28.
US President Joe Biden said Russian air strikes in Kyiv Sunday morning were "more of their [Russian] barbarism."
Biden was responding to a question by reporters at the G7 summit about Russian strikes that hit residential buildings in Kyiv this morning for the first time in weeks.
Germany is hosting this year's G7 annual summit — with leaders of the US, Canada, France, Italy, Japan, and the UK — from Sunday to Tuesday at the Elmau luxury resort in the Bavarian Alps.
German Chancellor Olaf Scholz, along with US President Joe Biden opened the summit Sunday, with Biden complimenting Scholz for stepping up to the challenges in Ukraine and saying it was important for them "to stay together."
European Council President Charles Michel condemned Russia's "hunger games" before the summit began, saying that Moscow was "using food as a silent weapon of war."
World leaders are set to discuss the war in Ukraine, food security, inflation, and climate change.
Russian Defense Minister Sergei Shoigu visited Russian troops in Ukraine on Sunday, Russia's Defense Ministry said. This was his first announced visit to Ukraine since Russia invaded the country in February.
The ministry released a video showing Shoigu stepping off a plane in dark green military fatigues and then conferring with military officials.
Shoigu also awarded medals to Russian soldiers. His location in Ukraine was not disclosed.
The US, UK, Canada and Japan announced Sunday that they will be banning Russian gold exports.
The joint action "will directly hit Russian oligarchs and strike at the heart of Putin's war machine," British Prime Minister Boris Johnson said in a statement.
The move by the four G7 powers is supposed to prevent Russian oligarchs from buying gold to reduce the impact of sanctions against Russia.
Gold accounts for about £12.6 billion (€14.6 billion, or $15.5 billion) to the Russian economy, and is a major export for the country.
Due to the sanctions imposed after Russia's invasion of Ukraine, many of the richest have converted their assets into gold to offset the impact of restrictions.
The London Bullion Market had already suspended six Russian refineries in action announced on March 7.
Given London's central role in the international gold trade and the parallel US, Japanese and Canadian action, "this measure will have global reach, shutting the commodity out of formal international markets," Britain said.
Britain's Ministry of Defense said most Ukrainian forces had withdrawn from their remaining defensive positions in the city of Sievierodonetsk.
The intelligence update said this was a significant development for Russia's offensive with a focus on the Donbas region.
The British report said Russian forces will also need to advance on the major center of Kramatorsk and secure major supply routes to the Donetsk city if Moscow wishes to occupy the whole of the Donbas region.
"Of course, it is a blow for the [Ukrainian] armed forces but also, I think it is a change of tactics for the Ukrainian side. Remember in Mariupol, Ukrainian soldiers were trapped in the Azovstal steel plant for months, and there has been criticism against the Ukrainian government as to why they didn't come to rescue the soldiers," DW Correspondent Emmanuelle Chaze said about the situation in Sievierdonetsk.
"So we could see it as a change of tactics from the Ukrainian side to regroup and be better prepared for further offensives from the Russian troops in the region of Luhansk, which has been under heavy shelling, with no respite for people living there," she added.
Kyiv Mayor Vitali Klitschko said on Telegram that multiple explosions had taken place in the central Shevchenkivsky district at around 6:30 a.m. local time (0330 UTC) on Sunday.
The district is home to universities, restaurants, and galleries.
"Ambulance crews and rescuers dispatched to the scene. Residents are being rescued and evacuated from two buildings," he said.
At least five people were wounded when a missile hit a building, the head of Ukraine's police force Ihor Klymenko said in a television interview.
Klitschko said the Russian missile strike was intended to "intimidate Ukrainians," ahead of the NATO summit in Madrid from June 28-30.
Klitschko later said two people were hospitalized and rescue efforts were ongoing as people were trapped under the rubble. He said a seven-year-old girl had been rescued from the rubble, and her mother was currently being removed as well.
Emmanuelle Chaze, DW's correspondent in Kyiv, said one person was found dead after the shelling. She tweeted a video of a building in ruins, saying five had been injured.
Anton Herashchenko, an advisor to the Ukrainian interior minister, said a nine-story apartment building was struck, and another rocket hit the grounds of a kindergarten.
The AFP news agency had reported four explosions, adding that a residential complex near the center of the city had been hit, causing a fire and a cloud of grey smoke.
Russia intends to supply nuclear-capable Iskander-M missile systems to Belarus in the coming months, President Vladimir Putin said on Saturday.
"In the coming months, we will transfer to Belarus Iskander-M tactical missile systems, which can use ballistic or cruise missiles, in their conventional and nuclear versions," Putin said in a broadcast on Russian television at the start of his meeting with Belarusian strongman Alexander Lukashenko in Saint Petersburg.
Putin also said Russia would help Belarus upgrade its fleet of Su-25 fighter jets to make them capable of carrying nuclear weapons.
British Prime Minister Boris Johnson on Saturday urged fellow G7 leaders not to "give up" on Ukraine four months into Russia's war. He also pledged fresh financial support for Kyiv.
In a late-night video address, Ukrainian President Volodymyr Zelenskyy said his country had been hit by 45 Russian missiles over the previous 24 hours, which he described as a cynical attempt to break Ukrainians' spirits.
The Ukrainian city of Sievierodonetsk in Luhansk Oblast is now completely under Russian control, a senior official from Russia's Defense Ministry has said.
Ukraine's largest LGBTQ rights event, KyivPride, has taken place jointly with Warsaw's annual Equality Parade owing to restrictions imposed in Ukraine amid Russia's invasion.
Buildings and infrastructure at a nuclear research facility in the northeastern city of Kharkiv have been damaged by Russian shelling, Ukraine's State Nuclear Regulatory Inspectorate said.
Russia is drawing on reservists to replenish its forces in eastern Ukraine, the head of Ukraine's military intelligence has told Reuters news agency.
Russia came down heavily on military sites in western and northern Ukraine with dozens of missiles targeting these locations.
mm, rm, tg, dh/fb (Reuters, AFP, AP, dpa)