Donald Trump's spokesman has denied that the US president refused to shake hands with German Chancellor Angela Merkel as they say side-by-side in the White House last week.

"I don't think he heard the question" posed by Merkel when she suggested they shake hands, in full view of press cameras, spokesman Sean Spicer told German weekly Der Spiegel published Sunday.

But Germany's top-selling Bild newspaper said that was "improbable", saying that throughout the meeting, Trump did not once look Merkel in the eye.

The pair did shake hands between podiums in a joint news conference during the visit.

The veteran German chancellor had arrived for her first meeting with Trump at a snowy White House hoping to reverse a chill in relations after Trump's incendiary election rhetoric, in which he called Merkel's acceptance of refugees a "catastrophic mistake" and suggested she was "ruining Germany."

The visit on Friday began cordially, with the pair shaking hands at the entrance of the White House. But later, sitting side-by-side in the Oval Office, Merkel's suggestion of another handshake went unheard or ignored by Trump – an awkward moment in what are usually highly scripted occasions.

German media pointed to the incident as another marker of the meeting's general icy mood between the cautious German chancellor and impulsive US president.

In a frequently awkward joint press conference in the East Room, Trump and Merkel showed little common ground as they addressed a host of thorny issues including NATO, defense spending and free trade deals.

For most of the 30 minutes, Merkel was stony-faced as Trump ripped into Washington's NATO allies for not paying for their "fair share" for transatlantic defense and demanded "fair and reciprocal trade" deals.