He said that could serve the new president well "as long as he has got good people around him and he has a clear sense of direction".
"There are certain things that make for good sound bites but don't translate into good policy".
"Because of the nature of the campaigns, and the bitterness and the ferocity of the campaigns, that it's really important to try to send some signals of unity, and to try to reach out to minority groups and women and others that were concerned about the tenor of the campaign", Obama said.
After the president met with Mr Trump last Thursday, The Wall Street Journal reports that Mr Obama realised that the Republican needs more guidance and promised to spend more time with his successor.
"My view is that if they can come up with something better that actually works and a year or two after they've replaced the Affordable Care Act with their own plan, that 25 million people have health insurance, and it's cheaper and better and running smoothly, I'll be the first one to say, "that's great, congratulations, '" Obama said".
Meanwhile, the appointment of far-right activist Stephen Bannon as the chief strategist of the administration has triggered a wave of protest from Democrats and civil rights activists.
"I think he recognizes that this is different", he said. "And hopefully then you correct for it", the president said.
The president earlier offered the Greeks reassuring words about the USA commitment to NATO, saying Democratic and Republican administrations alike recognize the importance of the alliance to the trans-Atlantic relationship.
The three-nation trip, during which Obama is expected to discuss regional and global issues with European leaders and attend a summit of leaders of the Asia-Pacific Economic Cooperation (APEC), was planned when his Democratic colleague Hillary Clinton seemed to be winning the race to the White House.
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Obama suggested he would continue to offer his advice.
Obama disclosed that he told Trump during their meeting that every action he takes has huge consequences.
Obama left the briefing room after the news conference.
Throughout the campaign, especially during the primaries in the first half of 2016, there were questions about the relationship between the Republican Party and the Trump campaign.
Obama appeared before reporters before leaving the United States on the last scheduled foreign trip of his presidency, to Greece, Germany and Peru.
HORSLEY: Well, one reason those European leaders are anxious is because of Trump's campaign rhetoric about North Atlantic Treaty Organisation, questioning whether that military alliance is still relevant, whether the USA could be trusted to come to the defense of countries that might not have spent enough money on their own military.
The two said the current relationship between Russian Federation and the U.S.is extremely unsatisfactory and agreed to further communicate by phone and arrange a meeting in person at a later date.
The President said that there were many diplomatic, military and humanitarian levers of USA power that made America the indispensable nation in the world and that status would continue.
And Tsipras noted, as Obama did at his press conference Monday, that though Trump had an "aggressive manner" during the campaign, the US president-elect is likely to act differently once in office.