"No one has an interest in protracted, adversarial negotiations," Obama said after meeting European Council head Donald Tusk and European Commission chief Jean-Claude Juncker at a NATO summit dominated by Britain's post-EU future.
The two-day NATO summit gathering 28 member state leaders in Warsaw was initially meant to focus on Russia after the Ukraine crisis but Britain's shock vote to quit the EU was on everyone's mind as the potential political, security and economic repercussions become clearer.
"Even as we face the difficulties of this moment we cannot lose sight of the extraordinary achievement that European integration continues to be," he said, praising the bloc's shared values of democracy and peace.
"For all the reasons I just mentioned, the United States has a strong and enduring interest in a united Europe."
British Prime Minister David Cameron, who is to meet Obama during the summit, stepped down last month after losing the Brexit referendum but he said starting negotiations with Brussels would be left to his successor, expected to be named in September.
Juncker, who has expressed dismay at the delay and pressed hardest for the talks to start as quickly as possible, said they would not be hostile.
"We have to engage in negotiations. And I'm not doing this, how I could say, in a hostile mood," Juncker said.
Tusk said the "political consequences of Brexit may be very serious" and stressed that "maintaining the closest relations is equally important".
