A senior aide to Costa made "brief" contacts with the Kremlin in recent weeks "to open communication channels", according to an EU official, speaking on condition of anonymity on Wednesday.
The EU has sought to isolate Russia diplomatically and economically since its 2022 invasion of Ukraine but European leaders have recently begun discussing the possibility of direct talks with Moscow about the war and broader security issues.
However, Costa's initiative drew criticism from some leaders at the two-day summit in Brussels, who said it was not co-ordinated with them and that the EU should focus on putting more pressure on Russia, according to people familiar with the closed-door discussions, which took place late on Thursday.
German Chancellor Friedrich Merz and French President Emmanuel Macron were not enthusiastic about the move, while Nordic and Baltic countries were most disturbed by it, according to the sources, speaking on condition of anonymity on Friday.
Several leaders also said there was no sign Russian President Vladimir Putin was ready to engage in serious talks so debates about who should take part in them on the European side were premature.
"Diplomatic channels with Russia don't matter if Russia doesn't want to do diplomacy," Latvian Prime Minister Andris Kulbergs said as he arrived for the second day of the summit on Friday.
A diplomat from a major European country said Costa had no mandate to open contacts.
"His talks were not co-ordinated with member states," the diplomat said.
As president of the European Council, Costa, a former Portuguese prime minister, chairs and organises summits of EU leaders and seeks to build consensus among member states.
He can also represent the EU externally.
Senior EU diplomats learned about Costa's initiative, which was first reported by Bloomberg, via the media rather than from his office, sources said.
Another EU diplomat said Merz and Macron had argued that any peace talks would be primarily about military capabilities and security guarantees for Ukraine, which would be a matter for individual European countries, rather than the EU.
However, some countries voiced support for Costa's move.
"Opening up a channel is not a mistake in our view," Irish Prime Minister Micheal Martin said on Friday.
An EU official said several leaders signalled that Costa is "the natural representative of the EU's interests".
The US has led diplomatic efforts to reach a peace deal between Ukraine and Russia, with the EU largely sidelined, despite Kyiv and Brussels saying it should play a role.
Merz, Macron and British Prime Minister Keir Starmer have also been discussing the war and relations with Russia in the so-called E3 format, which has annoyed other leaders such as Italian Prime Minister Giorgia Meloni as they are not included.
