President Barack Obama cautioned against dire predictions for Donald Trump's presidency Monday, saying his Republican successor faces a reality check if he tries to enact his most controversial campaign promises.

The outgoing Democratic leader made his comments at a wide-ranging news conference before he embarked on a farewell visit to Europe to reassure worried allies about a man he once warned was “unfit” to lead the United States.

Trump's election win last week over Hillary Clinton has been met with euphoria among his supporters, but also with a wave of protests across the nation that are unusual for the world's leading democracy.

The 70-year-old Republican billionaire - who takes office in just nine weeks - was holed up in his home office in Manhattan with his inner circle, working to shape his new administration.

While admitting that he had “concerns” about his successor, the message Obama delivered on Monday was designed to comfort those still ill at ease with Trump - and a lesson for the billionaire populist in the art of the presidency.

Trump, a real estate developer and reality TV star who has never held political office, has threatened to shake up America's most important international relationships.

But Obama said that deporting millions of immigrants, tearing up mutual defense treaties with Nato and Japan, and unraveling global deals on Iran's nuclear programme and the environment were not as simple as delivering tub-thumping rhetoric.

“Regardless of what experience or assumptions he brought to the office, this office has a way of waking you up,” Obama said.

“Reality has a way of asserting itself,” he added, offering his view that Trump is pragmatic rather than ideological.

US President Barack Obama (Getty)

Obama said that during a meeting with Trump at the White House last week, he had told the president-elect that his actions can move markets, tanks and public sentiment.

“I emphasised to him that, look, in an election like this that was so hotly contested and so divided, gestures matter,” Obama said.

“It's really important to try to send some signals of unity, and to reach out to minority groups or women or others that were concerned about the tenor of the campaign.”

“Do I have concerns? Absolutely. Of course, I have concerns. He and I differ on a whole bunch of issues. But the federal government and our democracy is not a speedboat - it's an ocean liner.”

Amid dire predictions about the end of the republic and the global order, Obama said that Trump's inexperience in politics and lack of intellectual baggage could be an asset.

“I don't think he is ideological. I think ultimately he is pragmatic in that way,” he told reporters at his first news conference since the Republican mogul defeated his Democratic rival Clinton in last week's presidential election.

“And that can serve him well as long as he's got good people around him and he has a clear sense of direction,” he continued.

Trump made his first two key appointments on Sunday - onetime Republican National Committee chair Reince Priebus will be his White House chief of staff, and anti-establishment media firebrand Steve Bannon his chief strategist.

The appointment of Bannon - the head of ultra-conservative Breitbart News who has championed the so-called “alt-right” perspective - has raised hackles, with Jewish and Muslim leaders expressing concerns.

Asked about Trump's choice of Bannon, Obama gave a pass. “It would not be appropriate for me to comment on every appointment that the president-elect starts making if I want to be consistent with the notion that we're going to try to facilitate a smooth transition,” he said.

More cabinet-level appointments will be rolled out this week, Trump's campaign manager Kellyanne Conway told reporters in New York.

Making the vital choices for Trump's cabinet has sparked intense infighting, CNN reported, with one source calling it a “knife fight.”

The New York mogul has also spent time calling world leaders as he begins to develop ties with America's allies - and adversaries.

“Getting his arms around foreign policy” is one of Trump's four top priorities, along with health care, immigration and taxes, as he prepares for his first 100 days as president, Priebus said.

“I see President-elect Trump being very calm and cool and collected. And prepared to lead the American people,” Priebus - seen as an establishment counter-weight to Bannon - told ABC's Good Morning America.

President Trump protests Show all 20 1 /20 President Trump protests President Trump protests Patrons hold a sign as people march by while protesting the election of Republican Donald Trump as the president of the United States in downtown Los Angeles, California Reuters President Trump protests Demonstrators rally following the election of Republican Donald Trump as President of the United States, in Oakland, California Reuters President Trump protests Demonstrators march following the election of Donald Trump as President of the United States Reuters President Trump protests Thousands of protesters rallied across the United States expressing shock and anger over Donald Trump's election, vowing to oppose divisive views they say helped the Republican billionaire win the presidency AFP/Getty Images President Trump protests Demonstrators protest outside the Chicago Theatre in Chicago, Illinois Getty President Trump protests A police officer aims a launcher after demonstrators threw projectiles toward a line of officers during a demonstration in Oakland, California Reuters President Trump protests An officer examines a vandalized police vehicle as demonstrators riot in Oakland, California Reuters President Trump protests Demonstrators take over the Hollywood 101 Freeway just north of Los Angeles City Hall in protest against the election of Republican Donald Trump as President of the United States Reuters President Trump protests A woman holds up a sign reading 'Trump you are an Idiot' as demonstrators gather during a protest against President-elect Donald Trump outside the City Hall building in Los Angeles, California EPA President Trump protests A masked demonstrator gestures toward a police line during a demonstration in Oakland, California Reuters President Trump protests Demonstrators protest against the election of Republican Donald Trump as President of the United States, near the Trump International Hotel & Tower in Las Vegas, Nevada Reuters President Trump protests Musician Lagy Gaga stages a protest against Republican presidential nominee Donald Trump on a sanitation truck outside Trump Tower in New York City Getty President Trump protests A woman yells as she takes part in a protest against President-elect Donald Trump in Seattle's Capitol Hill neighborhood AP President Trump protests A man dressed in red-white-and-blue sits on the curb during a protest against President-elect Donald Trump in Seattle's Capitol Hill neighborhood AP President Trump protests A protester sets off fireworks during a protest against President-elect Donald Trumpin Seattle's Capitol Hill neighborhood AP President Trump protests University of California, Davis students protest on campus in Davis, California, U.S. following the election of Donald Trump as President of the United States Reuters President Trump protests An Oakland police officer checks out damage after a window was broken by protesters at a car dealership in downtown Oakland, Calif AP President Trump protests A protester faces a police line in downtown Oakland, Calif AP President Trump protests President-elect Donald Trumpís victory set off multiple protests AP President Trump protests A fire burns during protests in Oakland, Calif AP

Obama said that Trump had already conveyed a “commitment to Nato” that seemed to run against his campaign promises.

“In my conversation with the president-elect, he expressed a great interest in maintaining our core strategic relationships,” Obama said.

During a visit this week to Europe, and then Peru for a summit with Asia-Pacific leaders, Obama said he would be able to tell allies “there is no weakening of resolve when it comes to America's commitment to maintaining a strong and robust Nato relationship.”

“This is a time of great change in the world, but America's always been a pillar of strength and a beacon of hope to peoples around the globe. And that's what it must continue to be,” he said.