On the last leg of his final European tour as president, Obama aimed to ease fears about the future of the transatlantic partnership and thank Merkel for her friendship during his two terms, White House officials said.
In a joint article to coincide with his arrival in Germany, Obama and Merkel appealed for ongoing cooperation on the basis of shared principles to fight climate change, ensure collective defence within NATO, and promote free trade.
"We owe it to our industries and our peoples - indeed, to the global community - to broaden and deepen our cooperation," they said, in a swat at the "America First" rhetoric favoured by Trump.
As Western leaders brace for potentially radical changes with Trump moving into the Oval Office in January, Obama wrapped up a visit to Athens yesterday warning that globalisation required a "course correction" to keep voters from drifting to extremes.
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"When we see people, global elites, wealthy corporations seemingly living by a different set of rules, avoiding taxes, manipulating loopholes... This feeds a profound sense of injustice," he said.
But in an extraordinary break with tradition for Germany, which long saw the US as its protector and closest ally, Merkel pointedly said cooperation must be based on shared democratic principles and respect for human dignity.
Analysts said the meeting could be seen as a kind of passing of the torch from Obama to Merkel, who the outgoing president has called "probably... My closest international partner".
In an interview with German public broadcaster ARD and news magazine Der Spiegel, Obama said Merkel had served her country well in the 11 turbulent years she has been in power.
"I am glad that she is there. I think the German people should appreciate her. Certainly I have appreciated her as a partner.