President-elect Donald Trump discussed foreign and domestic policy in a meeting at the White House, Barack Obama said.
Following the meeting in the Oval Office, Mr Trump said he had discussed "a lot of situations, including some difficulties" with the serving President - and said he looked forward to more meetings together.
Mr Obama said they talked about foreign and domestic policy, adding:
My number one priority in the coming two months is trying to facilitate the transition, that ensures the President-elect is successful.
I have been very encouraged by the interest in the President-elect Trump's wanting to work with my team on any 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 and work together to deal with the many challenges we face.
Mr Trump said it had been the first time the two men had met in person.
"I have great respect - the meeting lasted almost an hour and a half, it could have gone on for a lot longer," he said.
"It really - we discussed a lot of different situations, some wonderful and some difficulties. I very much look forward to dealing with the President in future, including council. He's explained some of the difficulties, some of the high-flying assets, and some of the great things that have been achieved."
US President-elect Donald Trump invited Theresa May to visit "as soon as possible" as they held their first talks by telephone on Thursday afternoon.
During the call, Mrs May congratulated Mr Trump on his election victory and they also spoke about the "special" UK-US relationship.
A Downing Street spokesman said: "President-elect Trump set out his close and personal connections with, and warmth for, the UK. He said he was confident that the special relationship would go from strength to strength."
Mrs May also expressed her commitment to strengthening bilateral trade and investment with the United States as Britain leaves the European Union, the spokesman added.
The call came ahead of Mr Trump's meeting with Barack Obama at the White House to discuss the handover process.
- Video report by ITV News Washington Correspondent Robert Moore
Angry protests have been taking place in some US cities across America against Donald Trump's election as the next president.
In Manhattan, demonstrators gathered outside Trump Tower to voice their discontent, with cries of "We reject the President-elect".
There were also protests in Oakland in California, Chicago, and Washington DC.
Thousands of people protesting Donald Trump's election as US president have taken to the streets in Oakland, California.
Crowds gathered in Frank Ogawa Plaza in downtown Oakland on Wednesday afternoon and demonstrated late into the night.
Some protesters set fires alight on the city's streets.
Meanwhile officers in riot gear blocked the protesters from marching on to the nearby Interstate 90.
The European Commission President has said he hopes US President-elect Donald Trump will outline his position on key issues such as trade, relations with Nato and climate change "in the next few months".
"We would like to know how things will proceed with global trade policy," Jean-Claude Juncker said at a business event in Berlin.
"We would like to know what intentions he has regarding the (Nato) alliance. We must know what climate policies he intends to pursue. This must be cleared up in the next few months."
Mr Juncker also said he did not expect the trade deal between the US and the European Union, currently being negotiated, to be done within the next two years.
The Chancellor has said he is confident Britain will have a "very constructive dialogue" with the US on trade when Donald Trump takes office as president.
Philip Hammond said: "We look forward to working with the new US administration.
He added: "We have very strong and close ties with the United States and as we begin the process of of negotiating our exit from the European Union, of course we will want to talk to the Americans about future opportunities for deepening our trade link with the United States."
Mr Hammond's comments came as he hosts talks in London with a Chinese delegation aimed at also deepening UK-China economic and trade relations.
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