During a 90-minute private meeting, Barack Obama said the two discussed foreign and domestic policy and how to ensure a smooth handover of power

Donald Trump was accorded a chilly but deferential welcome at the White House on Thursday as the president-elect met Barack Obama for a 90-minute private meeting in the Oval Office.

In the first stage of a 72-day transition process between Tuesday’s unexpected election victory and Trump’s inauguration on 20 January, Obama said the two men discussed “foreign and domestic policy” and how to ensure the handover of power went smoothly.

“I want to emphasise to you, Mr President-elect, that we now are going to do everything we can to help you succeed because if you succeed, then the country succeeds,” Obama told his successor during a brief photo opportunity afterwards.

A grinning Trump gave Obama a pat on the back as they got up to leave, and boasted to reporters of how long he had just spent in the Oval Office, though the president – more sombre-faced until then – jokingly advised him not to take any questions.

While they spoke, Trump’s wife Melania was shown around their new home in the official residence and East Wing by Michelle Obama, reportedly discussing what it was like to raise children in the White House.

Trump appeared to relish the welcome, though White House officials did not allow photographs of the traditional greeting outside. Obama appeared stiff and subdued throughout.

“This was a meeting that was going to last for maybe 10 or 15 minutes, and we were just going to get to know each other,” said Trump in the brief remarks to reporters he gave from an ornate armchair usually occupied by world leaders.

“We had never met each other. I have great respect. The meeting lasted for almost an hour and a half. And it could have – as far as I’m concerned, it could have gone on for a lot longer.”

Asked if he would seek advice from Obama in the future, despite intense criticism from both of them toward the other in the past, Trump described his political opponent as a “very good man”.

“We discussed a lot of different situations, some wonderful and some difficulties,” said the president-elect, according to the official White House transcript of their remarks. “I very much look forward to dealing with the president in the future, including counsel. He explained some of the difficulties, some of the high-flying assets and some of the really great things that have been achieved.”

Briefing reporters afterwards, press secretary Josh Earnest said he did not know what Trump had meant by “high-flying assets” and denied the Republican’s claim that only 10 minutes had originally been scheduled.

But he insisted the meeting was “a little less awkward than some might have expected” and tried to explain Obama’s comment that the meeting had been “excellent”.

“When you consider the profound differences between the two gentlemen and the fact they have never met before ... I think that qualifies as ‘excellent’,” said Earnest.

Washington has quickly adopted a deferential approach toward the future commander-in-chief, despite widespread demonstrations in major US cities since Tuesday’s election and reports of an increase in racist attacks aimed at immigrants.

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As votes from California and other Democratic-leaning states on the west coast were slowly processed on Thursday, Clinton was on track to exceed Trump’s share of the popular vote by 1.2%, fueling concern about the mandate for sweeping change.

Yet there were no protests visible outside the White House in the hour leading up to Trump’s arrival. One woman with a placard saying “stand up to racism” laid it on the ground as she was interviewed by a succession of media crews, though other protesters were expected during the meeting.

Dan Roberts (@RobertsDan) This was the only sign of dissent I could find outside the White House 45 mins before Trump arrives. Too busy being interviewed to pick up. pic.twitter.com/XndlSKvu8N

Instead, the traditional Marine guard stood stiffly outside the West Wing as Trump’s motorcade swept in from Ronald Reagan airport, where he left his trademark Boeing 757-200. The US Secret Service has announced a temporary no-fly zone for commercial aircraft over Trump Tower in New York, where the president-elect will continue to live for the next few weeks.

Trump’s motorcade arrived on the South Lawn at the White House, which is not visible to journalists or the public. He also refused to allow the usual presence of a pooled media representative with him as he travelled. Spokeswoman Hope Hicks said Trump would travel back to New York on Thursday night.

In a sharp change of tone, much of the US news media has treated Trump with the respectful approach usually granted to the US head of state when performing ceremonial duties, referring to the president-elect informally as PEOTUS.

During the Oval Office meeting, Ivanka Trump’s husband Jared Kushner – a likely top aide in the next administration – was escorted through the Rose Garden by White House chief of staff Denis McDonough.

Vice-president Joe Biden was due to meet with his successor, Mike Pence, while Trump headed to meet Republican congressional leaders Mitch McConnell and Paul Ryan on Capitol Hill. They have pledged to give him full support in repealing key Democratic legislation such as Obamacare and international climate change accords.

Trump’s election win has already ignited protests across the US, with thousands of demonstrators crowding into streets and surrounding his buildings in major American cities during the first night after the result.

The protests – in cities including New York City, Chicago, San Francisco, Oakland, Philadelphia and Seattle – erupted after the Democratic candidate, Hillary Clinton, lost the electoral college and presidential race on Tuesday night despite almost certainly winning the popular vote.

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As night fell in midtown Manhattan, people took over Sixth Avenue and marched by Trump Tower, carrying signs that read “Not my president”, “She got more votes” and “Hands off my pussy”, a reference to a leaked recording where Trump bragged that he could sexually assault women because of his fame. A number of arrests were made.

Protesters who had marched all the way from Union Square – 35 blocks downtown – continued past Trump Tower, with a crowd congregating in front of the president-elect’s building.

Behind the scenes there is also a bleak mood among many Democrats in the outgoing administration, but officially it has decided to emphasise small signs of progress in the tone adopted by Trump since his victory.

“I have been very encouraged by the, I think, interest in President-elect Trump’s wanting to work with my team around many of the issues that this great country faces,” said Obama. “And 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.”

Facebook Twitter Pinterest Donald Trump’s victory on Tuesday night has sparked demonstrations in major cities across the US. Photograph: Lucas Jackson/Reuters

The two also had specific conversations about how Obama would handle discussions with foreign leaders on an upcoming overseas trip. They also discussed ways of organising an effective team around the new president to handle future crises.

“They spent a large portion of the meeting discussing the importance of properly staffing and organising a White House,” Earnest, the press secretary, told reporters after the meeting.

He declined to answer questions about whether they discussed Trump’s promise to unwind much of the outgoing administration’s achievements over the last eight years.

“President Obama came away from the meeting with renewed confidence in the commitment of the president-elect to ensure a smooth transition,” said Earnest.

No staff were in the room during the meeting, but Earnest stressed it was unrealistic to expect the meeting to smooth over all that had gone beforehand.

“I feel confident in telling you that they did not resolve all of their differences, but I also feel confident in telling you that they did not try to resolve all of their differences.”

He said he was not aware of any additional meeting that has been scheduled but “wouldn’t rule out anything” after Trump spoke of wanting to hear Obama’s counsel.

It is thought the meeting in Washington on Thursday was the only time they have been in same room since Obama ridiculed Trump’s claims about his birthplace at a White House correspondents’ dinner in 2011.

Additional reporting by Sam Levin in San Francisco, Zach Stafford in Chicago and Scott Bixby in New York