Dmitry S. Peskov, Mr. Putin’s spokesman, confirmed the meeting in an interview and said both sides had agreed that they needed a political solution to de-escalate the crisis. He said that the conversation had been cordial and brief and that there were no immediate plans for another meeting. “They agreed on the need to stop the violence,” Mr. Peskov said. “It is a positive step – a very humble one, but it is positive.”

A White House official separately confirmed the discussion between Mr. Obama and Mr. Putin but did not immediately give details of the content. “It was an informal conversation, not a formal bilateral meeting,” said Benjamin J. Rhodes, Mr. Obama’s deputy national security adviser.

The conversation came after an awkward pas de deux between Mr. Obama and Mr. Putin, who initially seemed to be going out of their way not to acknowledge each other’s presence amid the world leaders gathered here. During the few minutes that they were before international journalists, Mr. Obama and Mr. Putin did not speak to each other, did not shake hands and in fact seemed eager not to encounter each other, much like divorced parents at a child’s graduation.