During a fractious presidential campaign, Trump had appeared to call into question a near 70-year-old security shield for US allies under NATO, and vowed to withdraw from hard-fought deals on the climate and Iran's nuclear programme.
The US president-elect's friendly disposition towards Russian President Vladimir Putin has also raised questions over his attitude toward Moscow's backing for President Bashar al-Assad in the Syrian war as well as Russia's role in the conflict in eastern Ukraine.
That meant "securing diplomatic resolution to the conflicts in Syria and eastern Ukraine", including putting the heat on Russia through sanctions until it met its commitments under a peace deal for Ukraine.
The leaders also affirmed the "importance of continued cooperation through multilateral institutions, including NATO".
Ahead of today's huddle in Berlin, Obama sounded a note of cautious optimism that Trump could change his position once he takes on the role as president.
"And if you're not serious about the job, then you probably won't be there very long. Because it will expose problems."
But Obama also stressed the importance of a united Europe, and urged the bloc not to take for granted the transatlantic relationship that has been built up over decades.
"The EU remains one of the world's great political and economic achievements, and those achievements should not be taken for granted," he said.
It opened with the burning question of the US-led coalition's battle against Islamic State jihadists in Syria and Iraq as well as Europe's migrant crisis, before delving into the Ukraine crisis, said an aide of Hollande about the talks that lasted just over two hours.
Citing both conflicts, Obama stressed on the eve of the meeting that he hoped Trump would be "willing to stand up to Russia where they are deviating from our values and international norms".
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