Obama said that they discussed organizational issued involved in setting up a White House, as well as domestic and foreign policy.
"And I have been very encouraged by the, I think, interest in President-elect Trump's wanting to work with my team around many of the issues that this great country faces, and I believe that it is important for all of us, regardless of party, and regardless of political preferences, to now come together, work together, to deal with the many challenges that we face," the President said. "And we want to make sure that they feel welcome as they prepare to make this transition. And most of all, I want to emphasize to you, Mr. President-elect, that we now are going to want to do everything we can to help you succeed because if you succeed, then the country succeeds."
Trump expressed gratitude for his meeting with Obama.
"We discussed a lot of different situations. Some wonderful and some difficulties. I very much look forward to dealing with the president in the future, including counsel. He explained some of the difficulties, some of the high-flying assets and some of the really great things that have been achieved," Trump told reporters. "So, Mr. President, it was a great honor being with you and I look forward to being with you many, many more times in the future."
Trump said that the meeting was only meant to last for a few minutes but went on for longer.
"We were just going to get to know each other. We had never met each other. I have great respect. The meeting lasted for almost an hour and a half. And it could have, as far as I'm concerned, it could have gone on for a lot longer," he said.
Obama said that Michelle Obama also met with Melania Trump.
White House Press Secretary Josh Earnest also addressed the meeting between the President and the President-elect with reporters, where he stressed that the conversation focused largely on a "smooth and peaceful transition." Earnest would not offer further details about the conversation when asked if Obama and Trump discussed Obamacare.
When asked if the two discussed Trump's comments on the campaign trail about jailing Hillary Clinton, Earnest said he would let Trump's team discuss "his end of the conversation."
And when asked if the meeting changed any of the concerns about Trump that Obama previously expressed, Earnest said that the meeting was focused on the transition and "was not convened to try to resolve the variety of concerns that President Obama had raised on the campaign trail.” When asked again, Earnest said that Obama and Trump did not "re-litigate their differences" during the meeting.
Earnest also told reporters that Trump's son-in-law, Jared Kushner, and spokeswoman Hope Hicks were at the White House for meetings on Thursday.
Watch a clip of Obama and Trump addressing the press via CNN: