In the Presidential campaign Trump exchanged controversial warm words with Putin - saying he had "strong control over a country" and "if he says great things about me, I'm going to say great things about him."
But speaking in a joint press conference with German Chancellor Angela Merkel, Obama said the relationship must not be unconditional.
Barack Obama said it was right to encourage a relationship with Russia (Photo: REUTERS) But he said fundamental values should be upheld (Photo: Getty)
Russia clashed with the US over foreign policy when it annexed Crimea and sent its military to Syria in support of divisive President Bashar Al-Assad.
Mr Obama said: "In order for us to solve many big problems around the world, it is in our interest to work with Russia.
"[However] on issues like Ukraine, on issues like Syria, we've had very significant differences. Putin and Trump have exchanged warm words (Photo: Getty)
"My hope is that the president-elect coming in takes a similarly constructive approach, finding areas where we can cooperate with Russia where our values and interests align.
"But that the president-elect also is willing to stand up to Russia when they are deviating from our values and international norms". The President appeared on his farewell tour with Angela Merkel (Photo: Getty) He suggested he would vote for Merkel if he could (Photo: REUTERS)
Obama and Merkel enjoyed a friendly meeting as two of the only major world leaders who have served for eight years or more.
"Chancellor Merkel is perhaps the only leader left among our closest allies who was there when I arrived," the President said.
And abandoning the premise of impartiality, he suggested he would vote for her if she attempted a fourth term in 2017