President Donald Trump had his chilliest summit yet with a foreign leader as he met with German Chancellor Angela Merkel today for the first time.

Talks began with a warm welcome outside the West Wing but turned cold as Trump blew off an attempted handshake in the Oval Office and disagreed publicly with Merkel on almost every major international issue.

Trump opened up a joint news conference that his daughter Ivanka attended with a slap at Merkel over her open-door refugee policy. Declaring that "immigration is a privilege, not a right," Trump said his first priority is to keep the country safe, the Daily Mail reports.

He also pushed for her country to live up to its NATO commitment, stressing the "need for our NATO allies to pay their fair share" for defence.

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Merkel told him it has always been her belief that it is has always been better to "talk to one another and not about one another" - a reference to the many disparaging statements Trump made on the campaign trail about her leadership.

As the press conference came to a close, Trump told Merkel "at least we have something in common, perhaps." They were both wiretapped by the previous administration, he implied.

The German chancellor did not react. She stood stoically behind a podium to Trump's right as the shocking statement was translated.

Trump had been asked about his claim that Barack Obama surveilled him and a follow-up allegation from his press secretary that Obama may have relied on British intelligence to do it.

That information came from a Fox News report that the British government slammed as "nonsense."

At his Friday (Saturday NZ time) news conference, Trump denied that his administration was impugning its overseas ally.

"We said nothing. All we did was quote a certain very talented legal mind who was the one responsible for saying that on television," Trump said of Fox's Judge Andrew Napolitano. "I didn't make an opinion on it. That was a statement made by a very talented lawyer on Fox. And so you shouldn't be talking to me. You should be talking to Fox."

President Donald Trump listens during a joint news conference with German Chancellor Angela Merkel. Photo / AP
President Donald Trump listens during a joint news conference with German Chancellor Angela Merkel. Photo / AP

Merkel is no stranger to Obama administration wiretapping. She herself was the subject of surveillance during his tenure. The explosive information came out in documents that were leaked by former NSA contractor Edward Snowden in 2013.

German newspaper Bild am Sonntag said Obama personally ordered the surveillance of the German leader. Der Spiegel reported that it began under the previous administration, in 2002, and ended in mid-2013.

Trump's administration has provided no proof that Obama monitored his calls or had his Justice Department surveil him or his business. His White House has pointed to news reports like the one on Fox to back up his charge.

After the US's spying on Germany was revealed, Obama apologised and told Merkel that his country would not eavesdrop on her again. The two eventually became close friends.

Trump struggled to put himself on similar footing with his German counterpart.

He had previously accused her of "ruining Germany" for allowing an influx of refugees from Syria into her country during his presidential campaign.

As the two sat down for their first face-to-face meeting since his election, Trump called it a "great honor" to meet her.

Helping to break the ice at a joint meeting with business executives was Germany's support for apprenticeship programs, something Trump, the former Apprentice star, couldn't help but point out.

"Both Germany and the United States are pioneering job-training programs," Trump said. "Here in the United States, companies have created revolutionary high-tech and online courses and, of course, for decades Germany has been a model for highly successful apprenticeship - that's a name I like, apprentice - apprenticeship programs," Trump said.

President Donald Trump and German Chancellor Angela Merkel participate in a joint news conference. Photo / AP
President Donald Trump and German Chancellor Angela Merkel participate in a joint news conference. Photo / AP

Trump was seated between Merkel and IBM's CEO Ginni Rometty. Execs from BMW, Siemens, and other companies also were there - as was daughter Ivanka Trump.

On the other side of Rometty sat Trump son-in-law Jared Kushner. Trump was also seated next to Vice President Mike Pence.

Trump's praise of the German apprentice model was in contrast to his ripping of the nation's immigration policy during the campaign. At one point, he predicted the German's would "riot" over Merkel's policy of accepting refugees.

The two sat awkwardly in the Oval Office earlier while photographers snapped photos.

While snappers asked for a handshake, the two sat a few feet apart, looking directly ahead, and did not take the opportunity.

But Trump offered warm words for Merkel at the end of his remarks. "I want to thank you very much. It's a great honor to have you in the White House," he said. "It's a great honor to have you in the United States, and I look forward to spending time with you," Trump said.

Trump said he wanted a close working relationship with Merkel if he were elected, despite their differences, and he'll find out today if such a thing is possible after all of the derisive comments that he made.

"You watch what happens to Angela Merkel, who I always thought of as a very good leader until she did this. I don't know what went wrong with her," said then-candidate Trump at an August rally in Virginia. "What went wrong? Angela, what happened?"

Since being elected, Trump has held up Germany as a reason for restricted travel and a ban on refugees.

President Donald Trump and German Chancellor Angela Merkel walk down the Cross Hall of the White House. Photo / AP
President Donald Trump and German Chancellor Angela Merkel walk down the Cross Hall of the White House. Photo / AP

After an Oval Office meeting this morning the leaders of the Western world's most influential counties played nice for the cameras, saying in English and German that it went well.

"We talked about lots of things," Trump told reporters, without going into detail.

A snowstorm forced them to postpone their plans for a meeting on Tuesday.

The itinerary includes discussions on strengthening NATO, fighting the Islamic State group and resolving Ukraine's conflict, all matters that require close cooperation between the U.S. and Germany, the White House said ahead of the visit.

Beyond those issues, today's sit-down was to be serve as a restart of a relationship complicated by Trump's rhetoric on the campaign trail.

Then, Trump seemed to care little about the potentially awkward ramifications were he to win. He invoked Merkel as a foil at his rallies, accusing his campaign rival, Hillary Clinton, of wanting to be "America's Angela Merkel." He lashed out at Time magazine when it named Merkel 'Person of the Year' in 2015 instead of him.

Still, Trump found ways to voice his respect. When a television station in September asked him to name a world leader he admired, he cited Merkel.

In his meetings with world leaders since the inauguration, Trump has adopted a more diplomatic public persona.

He recently spent a weekend bonding with Japanese Prime Minister Shinzo Abe, golfing and dining with Abe at his Mar-a-Lago estate in Florida. He has cultivated a closer friendship with Israeli Prime Minister Benjamin Netanyahu, whom he has known for years.

But Merkel is used to an altogether different type of American leader, having shared a strong bond with President Barack Obama.

She was the last of Obama's key European allies still in power when he left office. And as the leader of Europe's biggest economy and most stable government, Merkel emerged in recent years as the leading voice for a continent struggling with slow growth, identity issues and increased security threats after a string of terrorist attacks.

Reflecting their connection, Obama and his wife called Merkel and her husband on the day before Trump's inauguration to thank her for "her strong, courageous and steady leadership." It was Obama's final call with a foreign leader, his advisers said.

Merkel's first major encounter with Trump comes as she seeks a fourth term as chancellor in elections later this year. She has acknowledged the contest could be difficult and has stressed a need for stability after Britain's decision to leave the European Union.

She reportedly has studied Trump's speeches and policies in advance of her trip, eager to find areas for cooperation. Steven Keil, a fellow with The German Marshall Fund of the United States, said Merkel has little reason to dwell on Trump's past comments.

"Merkel is extremely pragmatic in her approach here, but she's also going to have some situations in which it will be tough for her to give too much," Keil said.

Trump has rattled European leaders with his "America first" mantra. He also backed Brexit and is sceptical of multilateral trade agreements. Merkel is expected to reiterate her belief that a strong EU remains in America's strategic and economic interests, a message she shared last month in Munich with Vice President Mike Pence.

She also is expected to bring with her a trade delegation that includes top executives of BMW and Siemens, employers of tens of thousands of Americans. Many live in Southern states that Trump won in the U.S. election.

Military matters may be testy. Trump declared NATO "obsolete" before telling European leaders the alliance remains important. But he is expected to reiterate calls for NATO members to meet a minimum commitment for defence spending. Only the U.S. and four other members currently reach the benchmark of spending 2 per cent of GDP on defence. Germany lags significantly behind.

"This is not a meeting to go through the list," said Heather Conley, senior vice president for Europe at the Center for Strategic & International Studies. "It's actually a really important meeting to set up the tone for the relationship in itself."

Conley said for all the lingering issues, Trump and Merkel's encounter held the promise of creating "a modus vivendi for these two leaders to really create a more stable framework for this critical relationship."