The tense ties between U.S. President Donald Trump and German Chancellor Angela Merkel were highlighted during their first face-to-face meeting, as both leaders could barely manage to keep their fundamental differences in policy and style under wraps.

Even though Merkel said she was "gratified" that the President pledged support for NATO and Trump insisting that he is a believer in free trade, their friction in opinion and believe could be seen, reports the Guardian.

In her remarks, Merkel also referred to past tensions with Trump, as she seeks to build a new relationship with the third US president she has encountered as German Chancellor.

Addressing the media through an interpreter, Merkel said, "It's always better to talk to one another than about one another," and defend her stance on refugees, to which Trump had taken a harsh stand during his presidential campaign.

Throughout his campaign, the US president had criticised the German leader's handling of the refugee crisis, saying her behaviour was "insane" and that she was "ruining Germany".

His backing for the Nato alliance, came with cautions. "I reiterated to Chancellor Merkel my strong support for Nato as well as the need for our Nato allies to pay their fair share for the cost of defence. Many nations owe vast sums of money from past years and it is very unfair to the United States. These nations must pay what they owe."

Business and trade were already a sore point of discussion for both nations as Trump had previously warned German car companies that he would impose a border tax of 35 percent on vehicles imported to the US market.

A German journalist challenged Trump over his potential to weaken the EU and his criticism of "fake news" in the media, to which Trump said sarcastically, "Nice, friendly reporter."

"First of all, I don't believe in an isolationist policy. But I also believe a policy of trade should be a fair policy and the United States has been treated very, very unfairly by many countries over the years, and that's going to stop. But I'm not an isolationist. I'm a free trader but I'm also a fair trader," he said.

Careful in her words and choosing to not openly disagree, Merkel said, "I believe globalisation ought to be shaped in an open-minded way but also in a fair way. Freedom of movement within the European Union, for example, is a very important element of our economic progress, of peace, has been for many decades."

Asserting that immigration and integration "have to be worked on" Merkel said that refugees should be given the opportunity to "shape their lives where they are", adding that these were issues that she and Trump had an "exchange of views" about.

When yet another German journalist asked Trump if he ever regretted certain tweets accusing his predecessor Barack Obama of wiretapping him, he replies saying, "Very seldom. I can get around the media when the media doesn't tell the truth."

Then taking a jesting note, he turned to Merkel saying, "This past administration, at least we have something in common perhaps," which provoked some laughter in the East Room of the White House, but none from the Chancellor whatsoever.

Trump's joke was in reference to the alleged tapping of Merkel's phone by the US National Security Agency - an incident that was reported to have infuriated Merkel when it came to light in 2013.

But the development which caught the world by storm is the awkward moment in the Oval Office before the press conference when the two leaders sat for photographers, who shouted a request for them to shake hands.

Merkel turned to Trump and asked: "Do you want to have a handshake?" The president ignored her and kept looking straight ahead, his hands clasped together. Merkel looked at the photographers with a half-smile, half-grimace.

By contrast, the President did shake hands with British Prime Minister Theresa May, Canadian Prime Minister Justin Trudeau and Japanese Prime Minister Shinzo Abe when they recently visited him in the Oval Office.