The Kyiv government, whose forces ring eastern Ukraine's cities of Donetsk and Luhansk, has urged remaining civilians to flee both via "corridors." Russia says it has a deal to deliver aid despite NATO and EU objections.
Ukraine's National Security and Defense Council on Monday said the "liberation" was "imminent" in both cities, including the largest, Donetsk, where rockets hit a jail, enabling some 100 inmates to flee.
Kyiv's security council spokesman, Andriy Lysenko, said "for civilians it is wise to leave" both cities through what he termed "humanitarian corridors."
According to Interfax Ukraine, Lysenko also said government forces would keep up momentum so insurgents could not receive new weapons.
The two cities are the last separatist strongholds, originally seized by rebels after the ouster of former president Viktor Yanukovych in February.
Officials in Luhansk, the second largest city held by pro-Russian rebels, said residents were "on the edge of survival," with no power or water, and fuel, food and medicines running short.
Russian aid bid rejected by NATO, EU
Russian Foreign Minister Sergei Lavrov said, meanwhile, that an aid delivery in cooperation with the International Red Cross had been agreed. Ukraine had previously objected to Russia's sending any aid into the region.
The Ukrainian presidential press service said US President Barack Obama had phoned President Petro Poroshenko and lent his support to an initiative for an international aid mission to the city of Luhansk under the aegis of the Red Cross and with the participation of the European Union, Russia, Germany and other countries.
"We agreed all details with the Ukrainian leadership." Lavrov said in Sochi, according to Russian news agencies. "I hope that the Western partners won't put a spanner in the works."
NATO chief Anders Fogh Rasmussen had earlier accused Russia - during an interview Monday with Reuters - of seeking a "pretext" to insert its troops into eastern Ukraine.
The European Commission said its head, Jose Manuel Barroso, had phoned Russian President Vladimir Putin and warned him to avoid any military action "under any pretext."
On Friday at the UN, the US had issued a similar warning to Russia not to use such convoys as a pretext to insert troops into eastern Ukraine. Britain and Germany also said they would not brook any such attempt.
Rasmussen on Monday said the military alliance saw no signs of a withdrawal of Russian forces from close to Ukraine's eastern border. He claimed Russia was "developing the narrative" for "illegal military operations" in Ukraine under the guise of humanitarianism.
Eastern Ukraine's new separatist leader, Alexander Zakharchenko, was quoted by the Interfax news agency on Monday as saying his fighters had enough weapons to resist the sieges by government forces.
Zakharchenko, a native of eastern Ukraine who replaced Russian national Aleksander Borodai as the leader of the self-proclaimed "Donetsk People's Republic," was quoted by Interfax as saying: "We are ready for a full-scale attack."
Donetsk's city administration said shelling of the city over the weekend had resulted in three people being killed and 16 being injured.
Rocket hit opens jail
City spokesman Maxim Rovinsky said a direct rocket hit on the jail had killed at least one inmate and left three others severely wounded.
A power cut disabled the jail's alarm system. He said 106 prisoners had fled.
"Extremely dangerous prisoners are not free," Rovinsky said.
In Kyiv, security council spokesman Lysenko blamed the prison break on separatist fighters, accusing them of shelling the correctional facility.
Casualties and refugee counts rise
Lysenko said 6 Ukrainian soldiers were killed since Sunday, raising Kyiv's military toll since April to 568 personnel killed.
UN agencies say in total more than 1,100 people have been killed, including government forces, rebels and civilians, in Ukraine over the past four months.
Rovinsky said an estimated 40,000 residents had already fled Donetsk. A further 20,000 were without electricity. The city had a pre-war population of 1 million.
Many Russian-speaking residents of eastern Ukraine distrust the new central government. Fighting began in April after Russia annexed Ukraine's peninsula of Crimea in March.
ipj/mkg (AP, AFP, Reuters, dpa)