US President Barack Obama and President-elect Donald Trump have met for the first time, setting aside the deep rancour that dominated the long campaign season as they discussed the transition to Trump's inauguration.

LISTEN ABOVE: Washington Post White House Bureau Chief Juliet Eilperin spoke with Larry Williams about Obama and Trump’s meeting

Their 90-minute meeting in the White House Oval Office, with no aides present, took place on Thursday, just two days after Trump's stunning defeat of former Secretary of State Hillary Clinton.

Obama, who vigorously campaigned for his fellow Democrat to succeed him, had repeatedly called Trump unfit for the president's office, while the Republican candidate had often denounced Obama's tenure as a "disaster".

But in separate post-election remarks on Wednesday both men appeared to seek to help the country heal from a bitterly divisive campaign season, and that tone continued into the White House meeting.

Seated next to Obama after their talks, Trump told reporters: "We really discussed a lot of situations, some wonderful, some difficulties."
He said Obama explained "some of the great things that have been achieved", but did not elaborate.

"It was a great honour being with you and I look forward to being with you many, many more times in the future," Trump said, with a tone of deference.

After Trump left the White House and travelled to Capitol Hill for meetings with Republican congressional leaders.

White House spokesman Josh Earnest told reporters, "The meeting might have been at least a little less awkward than some might have expected".

Obama said he and Trump, a real estate magnate who has never held political office, discussed a range of domestic and foreign policy issues.

Obama offered assistance to the New York businessman over the next couple months, and urged the country to unite to face its challenges.

In a possible early pivot by Trump, controversial campaign proposals, including his call to ban Muslims from entering the United States, have been removed from the president-elect's campaign website.

As the current president and next president huddled, White House chief of staff Denis McDonough was seen walking near the Rose Garden with Trump's son-in-law Jared Kushner, who like Trump is also a real estate developer, and other aides.

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

Trump said later after a meeting with House of Representatives Speaker Paul Ryan that he will work very rapidly on issues like healthcare and immigration.

"We are going to lower taxes, as you know," Trump said.

"I think we are going to do some absolutely spectacular things for the American people."

Meanwhile, in response to protests across the country, the White House said while Obama believes in the right of Americans to protest the election of Trump in a non-violent manner, but wants people to hear the message that "we're Americans and patriots" before Democrats and Republicans.