Britain's shock vote to leave the European Union dominated Obama's final NATO summit, which comes at what he called the most critical time for the military alliance since the Cold War.
Obama used the Warsaw summit to issue a clear message to key US allies Brussels and London to resolve their differences amicably.
"No-one has an interest in protracted, adversarial negotiations," he said.
But he said that while the British vote had "created uncertainty" about European integration, fears that it could destabilise the relationship between Europe and the United States were exaggerated.
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Obama said earlier in the Financial Times he was "confident" Britain and the EU could make an "orderly transition to a new relationship."
Britain would "continue to be a major contributor to European security," he predicted.
British Prime Minister David Cameron -- who is also at his last NATO summit after standing down after the Brexit vote -- insisted Britain would not play a "lesser role in the world".
"We are not turning our back on NATO," said Cameron, whose nuclear-armed nation is one of Europe's biggest contributors to the alliance.
In response to Obama's comments, the EU's Juncker toned down his previously tough position on Britain's need to start divorce proceedings immediately and said negotiations would not be in a "hostile mood."
Stoltenberg, Tusk and Juncker later signed a NATO-EU cooperation accord, laying out how the alliance can work with the EU.
Russia was meant to be the focus of the two-day meeting, with NATO preparing to endorse its biggest revamp since the end of the Cold War in response to Russia's 2014 intervention in Ukraine.