(CNN) -- A much anticipated encounter between President Barack Obama and his Russian counterpart, Vladimir Putin, came on the sidelines of a lunch held Friday to mark the 70th anniversary of D-Day.
But a conversation between Putin and Ukrainian President-elect Petro Poroshenko may have been more fruitful.
"We believe it's a good thing they were able to speak, but it's not a substitute for the steps it (Russia) needs to take to deescalate things, especially violence," a senior administration official said. "It's a positive thing that they spoke, but more needs to be done."
The official said Putin has publicly voiced support for Poroshenko, but "he's not taking steps to back that up."
Putin and Poroshenko's conversation included plans to discuss a cease-fire in the coming days, the office of French President Francois Hollande said.
"It would have to be mutual," the administration official said of the cease-fire. "Not just on the part of the people of Ukraine, but also the Russians."
During their informal aside, Obama told Putin that to reduce tensions in Ukraine, Russia must recognize Poroshenko as the country's legitimate leader and stop supporting separatists in eastern Ukraine.
Obama also told Putin that Russia must stop the flow of weapons across the border into Ukraine, Deputy National Security Adviser Ben Rhodes said.
Working with the Ukrainian leadership is the only way to reverse Russia's increasing isolation, Obama said, according to Rhodes.
"We didn't think it was the right time, place or circumstances to have a discussion," the senior administration official said. "We believe they haven't legitimately recognized Poroshenko."
The talk lasted 10 to 15 minutes.
Speculation had been brewing that the American and Russian leaders would meet, despite apparently elaborate steps taken by Hollande to avoid a tense encounter.
On Thursday, he dined with Obama before hosting a separate dinner with Putin.
The pair were also seated well apart for the D-Day lunch. With Hollande and the queens of Britain and Denmark between them, the two seemed unlikely to have to converse unless they wanted to.
The World War II commemorative events also brought Putin and Poroshenko together in their first face-to-face meeting.
Putin and Poroshenko shook hands before their informal exchange, Hollande's office told CNN.
No interaction was seen between Obama and Putin at that point.
'Lane of international law'
Speaking Thursday in Brussels, Belgium, Obama said he and Putin were likely to cross paths in France, although no formal meeting was planned.
Obama said then that if they spoke, he would give Putin the same message on Ukraine that he has given him in phone calls over past weeks and in his public statements.
Putin "has a chance to get back into a lane of international law," he said.
Obama said Putin could start by recognizing Poroshenko, stopping the flow of weapons over the border into Ukraine and ceasing Russian support for pro-Russian separatists in Ukraine.
Putin, in an interview with French television station TF1, did not discount the possibility of meeting with Obama.
"As for my relations with Barack Obama, I have no reason whatsoever to believe he is not willing to talk to the President of Russia," he said. "But ultimately, it is his choice. I am always ready for dialogue, and I think that dialogue is the best way to bridge any gaps."