David Jackson

USA TODAY

WASHINGTON — President Obama said he and successor-in-waiting Donald Trump had an "excellent conversation" Thursday as the intense rivals who defined the volatile 2016 election discussed the hand-off of the White House.

Just days after vicious attacks on the campaign trail, the two men spoke well of each other and shook hands for the cameras. Trump, who famously challenged the president's place of birth, called his predecessor "a very good man" following their Oval Office meeting.

Obama said his "number one priority" in the next two months in office is to facilitate the transition to the Trump administration. He said the two talked about "organizational issues," as well as domestic and foreign policies. "I believe that 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 told reporters.

In pledging a smooth transition, Obama told Trump that "we now are going to want to do everything we can to help you succeed — because if you succeed, then the country succeeds."

Trump — noting that the meeting ran long — said: "Mr. President, it was a great honor being with you, and I look forward to being with you many, many more times in the future."

The New York businessman also said: "We had never met each other. I have great respect."

The two shook hands for the cameras, but did not take questions from reporters.

Obama: Americans must support President-elect Trump

Heading into the meeting, Obama and Trump struck conciliatory notes in the wake of Tuesday's surprising election results, following a campaign of searing rhetoric.

"It's time for America to bind the wounds of division," Trump said during his victory speech early Wednesday.

Obama is "quite sincere about fulfilling the basic responsibility that he has to the American people and our democracy to ensure a smooth transition to the next presidency," said White House press secretary Josh Earnest.

After the meeting, Earnest said the two leaders did not resolve all of their differences, but did not try to either; their focus was a smooth transition.

An 'Obama era' crashes as Donald Trump takes White House

Trump followed up the meeting by heading to Capitol Hill to meet with another key player in his emerging presidency, Republican House Speaker Paul Ryan. The vice president-elect, Mike Pence, also attended the session with Ryan, who, like Obama, has had his share of differences with Trump. Afterward, Ryan said that "we had a fantastic, productive meeting about getting to work."

The president-elect also met with another powerful Republican, Senate Majority Leader Mitch McConnell of Kentucky.

Asked about his talks with lawmakers, Trump told reporters: "We have a lot to do. We're going to work very strongly on immigration, health care and we're looking at jobs, big league jobs."

Gearing up for his Jan. 20 inauguration, Trump is also starting to speak on the phone with an array of leaders from across the globe, from Japan to Turkey. British Prime Minister Theresa May congratulated Trump on his victory, and reminded the New York businessman of his "commitment in his acceptance speech to uniting people across America, which she said is a task we all need to focus on globally," according to a statement from May's office.

Trump invited May to visit him as soon as possible, the statement said.

Another world leader, Canadian Prime Minister Justin Trudeau, announced his government is prepared to re-negotiate parts of the North American Free Trade Agreement with Canada. During his campaign, Trump said existing free trade deals have shipped overseas.

The Trump team is also putting together possible picks for the Cabinet and White House staff.

While Obama and Trump spoke in the Oval Office, first lady Michelle Obama gave a tour of the residence to Melania Trump. During the campaign, Mrs. Obama criticized Trump over his lewd comments about women. Mrs. Trump, during her address to the Republican national convention, used lines cribbed from a speech the first lady had once given.

In preparing for his sit-down with Trump, the president said "it is no secret" that they have "some pretty significant differences." But the president added that he'd also had differences with his predecessor, George W. Bush, and they had a smooth transition. He said he has instructed aides 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."

One Trump backer and Obama critic, former House speaker Newt Gingrich, described the meeting between the president and his successor as "an amazing tribute to the power of the people."

Trump spent much of his insurgent campaign pledging to reverse and tear down Obama's legacy. He called for repealing and replacing the president's health care law, voiding the Iran nuclear deal and ripping up new business and environmental regulations.

On the stump, Trump also criticized Obama for campaigning so much on behalf of Democratic nominee Hillary Clinton, saying he should "do the job he's supposed to be doing."

In his campaign speeches, Obama cast Trump as an erratic and perhaps unstable political novice who shouldn't be allowed near the nuclear codes. "It's really bad being arrogant when you don't know what you're talking about," Obama said.

The Obama-Trump rivalry, intrinsic to the 2016 election, goes back years.

The Trump-Obama rivalry fuels 2016 campaign

During Obama's first term, Trump made a name for himself by becoming the de facto leader of the so-called "birther" movement, pushing the false idea that the president was not born in the United States. In this past campaign year, Clinton described the birther movement as a racist attack on the nation's first African-American president.

In 2011, Obama responded by producing a long-form birth certificate and mocking Trump at a high-profile press dinner as the New York businessman sat in the audience.

At the White House on Wednesday, Obama said he wants to make sure the presidential succession is "well executed because ultimately we're all on the same team."