President-elect Donald Trump said yesterday it was a “great honour” to meet United States President Barack Obama for transition talks at the White House.

Obama said he was “encouraged” by their “excellent” and “wide-ranging” conversation, which lasted for about 90 minutes..

Trump had questioned Obama’s US citizenship and vowed to dismantle his legacy.

During the campaign, Obama called Trump “uniquely unqualified”.

The businessman also called Obama “the worst president in the history of the United States

However, Obama said he was “rooting” for him after his shock defeat of Hillary Clinton.

After their meeting at the White House, 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.”

He said they had discussed domestic and foreign policy and he had been “very encouraged” by Trump’s interest in working with his team on issues facing the U.S.

Trump said he would “very much look forward” to interacting with President Obama in future

“I have great respect, the meeting lasted for almost an hour and a half, and it could’ve, as far as I’m concerned, it could’ve gone on for a lot longer,” the president-elect said.

“We discussed a lot of different situations – some wonderful and some difficulties.”

Trump, who said he had never met Obama, called him a good man and said the two had discussed both “wonderful” things and the “difficult” challenges the country was facing.

On Wednesday, thousands took to the streets of major US cities denouncing Mr Trump after his shock defeat of Hillary Clinton.

White House spokesman Josh Earnest has insisted Obama is sincere about ensuring a smooth handover.

With the Republicans now holding a majority in both chambers of the US Congress, Mr Trump can more easily target key Obama initiatives like such as his healthcare reforms.

The president-elect’s transition team for the 10-week period until inauguration will be led by Chris Christie, Governor of New Jersey.

Former New York Mayor Rudy Giuliani is a leading contender to serve as attorney general and Representative Michael McCaul of Texas, chairman of the House Committee on Homeland Security, is a top choice for Homeland Security secretary, according to people familiar with the matter. Senator Jeff Sessions of Alabama is interested in serving as defense secretary, the people said.

Mr Trump, who has never held elected office, has said his immediate priorities will be restoring the country’s infrastructure and doubling its economic growth

Trump flew from New York on his private jet and landed at Reagan National Airport, just outside the nation’s capital.

The president-elect was accompanied by his wife, Melania, who had a meeting with First Lady Michelle Obama.

His motorcade arrived at the White House’s South Lawn, where reporters weren’t able to observe the two men greeting each other, shortly before 11 a.m. New York time.

White House Chief of Staff Denis McDonough was seen walking with Trump’s son-in-law, Jared Kushner, a close adviser to the president-elect, on the South Lawn while Obama and Trump met. Obama and Trump met alone but posed for photographs with a handful of senior aides after the meeting.

White House press secretary Josh Earnest told reporters the meeting was “robust” and “valuable.”

“It is no secret that the president-elect and I have some pretty significant differences,” Obama said in the Rose Garden on Wednesday. “But remember, eight years ago, President Bush and I had some pretty significant differences.”

Obama said he had told his “team to follow the example that President Bush’s team set eight years ago, and work as hard as we can to make sure that this is a successful transition for the president-elect.”

Trump didn’t mention Obama in his victory speech early Wednesday. He called for unity, saying, “It’s time for America to bind the wounds of division.”

“I pledge to every citizen of our land that I will be president for all Americans,” Trump said.

Neither man has addressed post-election protests in several major cities, including New York and Washington, where demonstrators have criticized Trump’s inflammatory rhetoric about African-Americans, Latinos, women, and Muslims.