WASHINGTON — For months, President Obama said that Donald J. Trump was unqualified, temperamentally unfit and a threat to the republic who should never be president.
For years, Mr. Trump questioned Mr. Obama’s birthplace and legitimacy, branded the nation’s first black president weak and called his tenure a disaster.
On Thursday at the White House, the once-unimaginable happened: The two men met face to face for the first time for a 90-minute discussion in the Oval Office and shook hands, making a public show of putting their bitter differences aside.
“I want to emphasize to you, Mr. President-elect, that we now are going to want to do everything we can to help you succeed because if you succeed, then the country succeeds,” Mr. Obama told Mr. Trump after the meeting as the two sat side by side two days after Mr. Trump’s stunning election upset imperiled Mr. Obama’s legacy. The president called the conversation “excellent” and said he had been “encouraged” by Mr. Trump’s interest in working with him and his team.
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Mr. Trump, who appeared nervous and uncharacteristically subdued beside Mr. Obama, called the president “a good man.” He said that the meeting was “a great honor” and that their conversation had lasted far longer than he would have expected.
“I have great respect,” Mr. Trump said, turning to face Mr. Obama. “We discussed a lot of different situations, some wonderful, and some difficulties. I very much look forward to dealing with the president in the future, including counsel.” Given that Mr. Trump has never held elective office or served in government, some administration aides suggest that Mr. Obama could play a larger-than-usual role in acquainting Mr. Trump with the demands of the office.
“The meeting might’ve been at least a little less awkward than some might have expected,” Josh Earnest, the White House press secretary, said. Aides said that the two men discussed foreign and domestic policy issues that Mr. Trump would need to deal with on Day 1 in the Oval Office. As early as Friday, the president-elect will get a version of the President’s Daily Brief, a classified compilation of all threats facing the United States and other highly significant intelligence information.
Mr. Trump’s trip was surreal for many Republicans and Democrats in Washington, who never expected to see the real estate executive and reality television star in an Oval Office meeting to begin preparations to lead the most powerful nation in the world. Mr. Trump, whose campaign drew support from white supremacist groups, sat just in front of a bust of the Rev. Dr. Martin Luther King Jr. in the Oval Office.
Outside in the Rose Garden, reporters could see Denis R. McDonough, the White House chief of staff, emerge from the West Wing talking in hushed tones with Jared Kushner, the president-elect’s son-in-law and adviser. The two then headed off for a stroll around the South Lawn. Nearby, aides to Mr. Trump snapped photographs of one another in the White House colonnade, standing in the spot where a crowd of shocked White House aides, some openly crying, had watched the day before as Mr. Obama called for national unity after Mr. Trump’s victory.
The Oval Office meeting was the centerpiece of a marathon day in the capital for Mr. Trump, his first since winning the presidency. His wife, Melania, had tea with Michelle Obama in the White House residence and took in the view of the Washington Monument from the Truman Balcony. White House aides said the two women talked about raising children in the White House.
“We want to make sure that they feel welcome as they prepare to make this transition,” Mr. Obama said of the Trumps.
Later on Capitol Hill, after meeting with Republican congressional leaders who will hold sway over enacting his agenda, Mr. Trump strode with Representative Paul D. Ryan of Wisconsin, the House speaker, to a balcony overlooking the platform on the west side of the Capitol where he will be sworn in on Jan. 20, 2017, peering out to the National Mall below.
“Really, really beautiful,” he said of the view.
The president-elect arrived in the late morning from New York at Reagan National Airport in his trademark jet with the name Trump emblazoned on its side, and then rode with his wife in a black, armored sport utility vehicle in a motorcade that moved swiftly through Washington. By midafternoon, crowds had gathered on a crisp autumn day on both sides of Pennsylvania Avenue next to the Trump International Hotel, where barricades were set up. Police officers were lined up on motorcycles, officers on horses patrolled the area, and tourists taking photographs mingled with camera crews.
Mr. Trump and his wife had lunch with Mr. Ryan at the Capitol Hill Club, a peace summit meeting after Mr. Ryan had offered tepid support for the Republican nominee during the campaign and Mr. Trump had branded him a “weak and ineffective leader,” threatening retribution.
Later, after a meeting in Mr. Ryan’s office in the Capitol, Mr. Trump said that he was excited to begin carrying out an agenda to address immigration, health care and tax cuts. Investors, apparently buoyed by the prospect of those tax cuts as well as increased infrastructure spending, sent the Dow Jones industrial average to a record high on Thursday.
“We’re going to do some absolutely spectacular things for the American people,” Mr. Trump said. “We’re going to lower taxes, as you know, we’re going to fix health care and make it more affordable and better. We’re going to do a real job for the public.”
Mr. Trump also met for about an hour with Senator Mitch McConnell of Kentucky, the majority leader.
“We are looking at jobs,” Mr. Trump told reporters as he left. “Big-league jobs.”
The meetings unfolded as members of Mr. Obama’s staff were starting the business of handing over the vast bureaucracy of the federal government to Mr. Trump’s staff. Speculation swirled over possible appointments in the Trump administration, with Stephen K. Bannon, the conservative provocateur and Mr. Trump’s campaign chief, and Reince Priebus, the Republican National Committee chairman, being mentioned as possible picks for chief of staff.
Top advisers to Mr. Obama have spent months preparing for the transition, a complex venture condensed into the 72 -days before the inauguration. It is up to them and the Trump team to set it in motion, pairing Obama administration staff members with representatives of the president-elect for crash courses in the workings of the White House and federal agencies.
Mr. Obama said Wednesday that he had instructed his staff to follow the example set by President George W. Bush in 2008 and provide a professional and smooth transition for Mr. Trump’s team, despite the policy differences that separate the president and his successor. For all the public drama and division of the presidential campaign, Mr. Obama’s aides have since July been quietly working with advisers to Hillary Clinton and Mr. Trump to plan for the passing of power.
But the crush of information may be onerous, particularly when it comes to Mr. Trump’s task of hiring 4,000 political appointees over a matter of weeks. Saddled with an antiquated personnel system when Mr. Obama was elected in 2008, his aides moved this year to build a new one designed to make it easier to track the positions, as well as the applicants and their personal and professional information.
In December, Mr. Obama’s team plans to hold the first of two war-gaming exercises to prepare Mr. Trump and his staff for a potential national security crisis. The second simulation for Mr. Trump is set for January, days before he officially gains access to the nuclear codes.