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Angela Merkel and Emmanuel Macron had suggested inviting the Russian president for talks. Leaders have though agreed new funding for the migration pact with Turkey.
EU leaders agreed Friday to plan for sanctions against Russia, but rejected a push for a summit with Russian President Vladimir Putin.
At the EU summit in Brussels, France and Germany had called for direct talks with Putin.
However, EU leaders failed to reach and agreement on such a summit. In a statement, they said that "they will explore format and conditionalities of dialogue with Russia" but did not mention a summit.
The statement also called on EU High Representative for Foreign Affairs Josep Borrell "to present options for additional restrictive measures, including sanctions" against Russia.
"We defined again under what conditions we are prepared to work and communicate more closely with Russia... There was no agreement today on an immediate leaders' meeting," German Chancellor Angela Merkel said after meeting EU leaders.
Prime Minister Andrej Babis' Czech Republic has been named, along with the US, as an 'Unfriendly State' by Russia
Merkel said the 27-member bloc needed direct dialogue with Russia because "conflicts can best be solved if you also talk to each other."
French President Emmanuel Macron said warmer ties with Moscow were "necessary for the stability of the European continent."
"We cannot remain in a purely reactive logic with regards to Russia," he said.
The bloc has not held a summit with the Russian leader since 2014 amid an ongoing rift over the annexation of Crimea
European-Russian ties have also been strained over the poisoning of opposition figure Alexei Navalny, who is currently imprisoned in a penal colony.
But the suggestion of closer ties with Putin has already created splits in the EU and came as a surprise to some EU governments. Two senior diplomats told DW that they first learned of the plan from the media.
Latvian Prime Minister Krisjanis Karins said there would be "difficulties" in seeking to build trust with the Russian government.
"The Kremlin understands power politics. The Kremlin does not understand free concessions as a sign of strength," Karins told journalists.
Lithuania, another Baltic state, was also cool on the idea floated by Paris and Berlin.
"If without any positive changes in the behavior of Russia, we will start to engage, it will send very uncertain and bad signals to our partners," the country's president, Gitanas Nauseda, said.
"It seems to me like we try to engage a bear to keep a pot of honey safe," he added.
Dutch Prime Minister Mark Rutte said he would boycott any direct EU meeting with Putin, citing the downing of the MH17 flight over Ukraine in July 2014.
Nearly 300 people died in the disaster, most of them Dutch citizens. A Dutch investigation blamed pro-Russian separatists for shooting down the plane.
Merkel also said EU leaders agreed to provide Turkey with around €3 billion ($3.6 billion) in financial aid to stem migration.
Turkey had agreed to keep migrants from reaching the EU in 2016 in exchange for financial aid from the bloc.
Turkey currently shelters 3.7 million migrants from the war in Syria.
Merkel said earlier in the week that the financial humanitarian aid given to Ankara should be shifted to socio-economic assistance, as some of the migrants in Turkey have been there for 10 years.
Hungarian Prime Minister Viktor Orban's government came under fire over legislation that banned LGBTQ content from being handed out in schools.
European Commission President Ursula von der Leyen this week branded the bill "a shame" that contradicts the fundamental values of the European Union and threatened to take Hungary to court.
Merkel said the EU leaders and Orban had a "very, very frank discussion."
"We all made it very clear here what fundamental values we are pursuing" and the European Commission "will now continue to deal with the Hungarian law."
Orban, however, remained unrepentant.
"This is not against homosexuality, any sexual interference. It's not about homosexuals," he said. "It's about the right of the kids and the parents."
Orban vowed not to withdraw the legislation.
"For me, Hungary has no place in the EU anymore," Dutch Prime Minister Rutte said ahead of the meeting.
Irish Prime Minister Micheal Martin said the bill broke "a fundamental value of the European Union" while Luxembourg's Prime Minister Xavier Bettel called it "unacceptable."
Leaders from 17 EU countries on Thursday signed a letter slamming "threats against fundamental rights, and in particular the principle of non-discrimination on grounds of sexual orientation."
The issue has been front and center of European politics this week after UEFA, Europe's football governing body, rejected a plan by Munich to light up its stadium in rainbow colors for a Germany-Hungary match on Wednesday.
Orban had been set to attend, but he decided to skip the game that ended in a 2-2 draw and saw Hungary eliminated from the European Championship.
jf, wd/rt (AFP, AP, Reuters)