US President Barack Obama and President-elect Donald Trump met on Thursday for the first time, setting aside the deep rancor that dominated the long campaign season to discuss the transition to the Republican's inauguration on January 20.

Their 90-minute meeting in the White House Oval Office, with no aides present, took place just two days after Trump's stunning election victory over Hillary Clinton, Obama's former secretary of state.

Obama, who vigorously campaigned for his fellow Democrat to succeed him, had repeatedly called Trump unfit for the president's office, while the businessman had often dubbed Obama's eight-year tenure a "disaster."

Source: b'Obama and Trump were cordial throughout the meeting | Source: Reuters'

But in separate post-election remarks on Wednesday, both men appeared to seek to help the country heal from a bitterly divisive campaign, 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 really great things that have been achieved," but did not elaborate.

"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, with a tone of deference.

Source: b'Obama had said throughout that Trump was unfit to be president | Source: Reuters'

Trump, a real estate magnate who has never held political office, later met congressional leaders, including US House of Representatives Speaker Paul Ryan, a Republican who has had a strained relationship with Trump.

"A fantastic day in D.C. Met with President Obama for first time. Really good meeting, great chemistry," Trump said on Twitter late on Thursday.

Amid the efforts to bury hatchets, there were protests in a string of U.S. cities against Trump for a second day on Thursday as demonstrators expressed concern that Trump's election would be a blow to civil rights.

"Just had a very open and successful presidential election. Now professional protesters, incited by the media, are protesting. Very unfair!" Trump tweeted.

Obama said he had offered assistance to Trump over the next couple of months, and urged the country to unite to face its challenges.

"We now are going to want to do everything we can to help you succeed because if you succeed, then the country succeeds," Obama said, adding he and Trump discussed a range of domestic and foreign policy issues and details related to the transition period.

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

The two men's relaxed, cordial demeanor in front of the cameras was in stark contrast to the months of harsh rhetoric during the campaign.

Source: b'Trump had criticised the protests against his election | Source: Reuters'

Trump used Obama as a punching bag during his campaign speeches, repeatedly attacking the president's policies from healthcare to an Iran nuclear deal. Both Obama and first lady Michelle Obama attacked Trump as temperamentally unfit for the White House and dangerously unprepared to have access to U.S. nuclear codes.

Asked at a White House briefing on Thursday whether the meeting had eased any of the concerns about Trump that Obama expressed during the campaign, Earnest said: "The president was never in a position to choose a successor. The American people chose his successor."

Thursday's start at fence-mending also included meetings between Vice President Joe Biden and his future successor, Pence, and between the current and future first ladies.

Michelle Obama met privately with Trump's wife, Melania, in the White House residence. Michelle Obama has raised two daughters in the White House and the Trumps have a son, 10 year-old Barron. The two women discussed raising children at the White House, Earnest said.

"Melania liked Mrs. O a lot!," Donald Trump said on Twitter.