Donald Trump has apparently refused to shake Angela Merkel's hand during a joint appearance at the White House.

The pair held an awkward meeting that could help determine the future of the transatlantic alliance and shape the working relationship between two of the world's most powerful leaders.

While the President greeted the German leader with a handshake upon her arrival at the White House, he appeared to ignore requests to do so as the pair sat together later in front of TV cameras.

In footage of the photo opportunity, as photographers call for the two to shake hands, Ms Merkel can be heard saying: "Do you want to have a handshake?"

Mr Trump briefly turns towards her, but continues sitting with his legs apart and hands together.

She then turns back to face the cameras, smiling thinly.

Despite the seemingly frosty nature of the joint appearance, both leaders described their meeting in brief remarks to reporters as having been very good.

The meeting is consequential for both sides.

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Ms Merkel, who officials say has prepared carefully for the encounter, is likely to press Trump for assurances of support for a strong European Union.

Mr Trump, who as a presidential candidate criticised Merkel for allowing hundreds of thousands of refugees into Germany, will seek her support for his demand that North Atlantic Treaty Organisation nations pay more for their defence needs.

Relationship building is a less overt but important agenda item. Ms Merkel had close relations with Trump's Democratic and Republican predecessors, Barack Obama and George W Bush, and she is likely to seek a strong working relationship with Mr Trump despite major policy differences and wariness in Germany about the former New York businessman.

He spent a good part of 2016 criticising the Chancellor, accusing her of "ruining" Germany for allowing an influx of refugees from Syria.

"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 Mr Trump at an August rally in Virginia. "What went wrong? Angela, what happened?"

Then, Mr Trump seemed to care little about the potentially awkward ramifications were he to win. He invoked Ms 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 Ms Merkel "Person of the Year" in 2015 instead of him.

Mr Trump, at the time, did find ways to voice his respect. When a television station in September asked him to name a world leader he admired, he cited Ms Merkel.

"Those who know the Chancellor know that she has a knack for winning over people in personal discussions. I am sure that Donald Trump will not be immune," said Juergen Hardt, a conservative lawmaker who helps coordinate transatlantic relations for the German government.

Mr Trump is eager to see follow-through on his demand that European countries shoulder more of the burden of paying for the Nato alliance, which he has criticised.

He will also seek ideas from Ms Merkel on how to deal with Russian President Vladimir Putin, a leader Ms Merkel has dealt with extensively and whom Mr Trump, to the consternation of Republican and Democratic lawmakers, has praised.

"The President will be very interested in hearing the chancellor's views on her experience interacting with Putin," a senior administration official told reporters.