Donald Trump has held a 90-minute meeting with President Barack Obama in the White House to discuss the transition of power after the Republican's upset election victory.

The President-elect told reporters: "We really discussed a lot of situations, some wonderful, some difficulties."

He said Mr Obama explained "some of the great things that have been achieved".

Mr Trump, elected on Tuesday to his first public office, said he looked forward to more meetings with Mr Obama, who he said he had never met before.

"As far as I'm concerned it [the meeting] could have lasted a lot longer," Mr Trump said.

"I very much look forward to dealing with the President in the future, including counsel.

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"Mr President, it was a great honour being with you, and I look forward to being with many more time in the future," he added, calling Mr Obama "a very good man".

Mr Obama promised said he would do everything he could to help the billionaire businessman succeed when he takes office on January 20.

"I have been very encouraged by an interest in President-elect Trump's wanting to work with my team around many of the issues that the country faces," Mr Obama said.

"My number-one priority in the coming two months is to try to facilitate a transition that ensures our President-elect is successful."

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First Lady Michelle Obama met privately with Mr Trump's wife, Melania, in the White House residence.

"Michelle's had the chance to greet the incoming first lady, and we've had an excellent conversation and want to make sure they feel welcome," Mr Obama said.

"We now are going to want to do everything we can because if you [Trump] succeed the country succeeds."