WASHINGTON — Barack Obama and Donald Trump on Thursday put past animosity aside during a 90-minute White House meeting designed to quell fears about the health of the world’s pre-eminent democracy.

As protests against the Republican property mogul’s shock election rumbled across US cities and world capitals contended with a suddenly uncertain world order, Obama and Trump vowed to carry out a smooth transition of power.

After a nasty campaign that culminated in the election of a 70-year-old billionaire who has never held public office and who gained power on a far-right platform, the message was: this is business as usual in a democracy.

The outgoing Democratic president and his successor huddled one-on-one in the Oval Office, for what Obama characterised as an "excellent conversation" and then put on a remarkably civil joint public appearance.

"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," Obama said.

Trump appeared more subdued than usual, and was unusually cautious and deferential in his remarks.

"Mr President, it was a great honor being with you," Trump said, calling Obama a "very good man".

The meeting, which came less than 36 hours after Trump’s shock election victory over Democrat Hillary Clinton, had the potential to be awkward.

After all, Trump championed the so-called "birther movement" challenging that Obama was actually born in the United States -- a suggestion laden with deep racial overtones -- only dropping the position recently.

And if the president-elect fulfills his campaign promises, he will unravel almost all of Obama’s signature achievements.

Trump -- who previously called Obama the "most ignorant president in our history" -- said he looked forward to receiving the president’s counsel.

Obama -- who previously said Trump was a whiner and "uniquely unqualified" to be commander-in-chief -- vowed his support.

He told Trump that his administration would "do everything we can to help you succeed, because if you succeed, then the country succeeds."

The two men ended the improbable and historic White House encounter with a handshake and refused to take questions, appearing to find common cause in their opinion of the press.

"Here’s a good rule. Don’t answer questions when they just start yelling," Obama told Trump.

Current, future first ladies

While their husbands were getting acquainted, First Lady Michelle Obama also had a sit-down at the White House with her soon-to-be successor, Melania Trump.

Vice President Joe Biden, meanwhile, met in his West Wing office with Trump’s running mate, Mike Pence, the new vice-president-elect.

White House officials said that Obama and Trump discussed a range of issues including global hotspots and the president’s meetings next week abroad with leaders from Germany, Greece and across the Asia-Pacific.

On that trip, Obama is likely to be inundated with panicked questions about America’s role in world affairs.

The White House hopes that by rolling out the red carpet for Trump, they can bind him to some of the conventions of the office.

Trump then traveled to Capitol Hill to meet Republican leaders who had been at best cool to him winning their party’s nomination.

The president-elect proclaimed that health care, border security and jobs will be his top three priorities when he moves to the White House next January.

He held talks with House Speaker Paul Ryan and then with Senate Majority Leader Mitch McConnell.

"We had a very detailed meeting," Trump told reporters. "As you know, health care -- we’re going to make it affordable. We are going to do a real job on health care," he said.

Trump made repealing Obamacare, and building a border wall between the United States and Mexico, pillars of his presidential campaign.

Trump said he and the Republican majority in Congress were going to accomplish "absolutely spectacular things for the American people," adding he was eager to get started.

Afterwards, following an hour-long meeting with McConnell on the other side of the Capitol, Trump stood at the Senate majority leader’s side and stressed that "we have a lot to do."

"We’re going to look very strongly at immigration," he said.

"We’re going to look very strongly at health care, and we’re looking at jobs - big league jobs." — AFP