President Donald Trump is in trouble whether his claim to have been wiretapped during the last months of the Obama administration is true or not, a senior Democratic senator has said.

Senate minority leader Chuck Schumer was speaking on NBC's Meet The Press on Sunday, days after calling for Attorney General Jeff Sessions to step down over the controversy surrounding his contact with a Russian ambassador.

But he said "if it's true it's even worse" for Mr Trump because it meant a judge had thought him or his staff worth investigating.

The President alleged in a string of angry messages on Saturday that his predecessor had ordered his New York office be put under surveillance “just before the victory”. He called Mr Obama a “bad (or sick) guy” and likened the supposed move to “Nixon/Watergate”.

Mr Schumer said: "If he falsely spread this kind of misinformation, that is so wrong it's beneath the dignity of the presidency, it is something that really hurts people's view of government. It shows this President doesn't know how to conduct himself.

"On the other hand, if it's true it's even worse for the President because that means that a federal judge, independently elected, has found probably cause that the President, or people on his staff, have had probable cause to have broken the law or to have interacted with a foreign agent.

"That's serious stuff so either way the President makes it worse with his tweets. Either way ... the President's in trouble."

The President's unsubstantiated claim appeared to have originated in a conservative radio broadcast, later written up on Breitbart, the Trump-backing right-wing website headed until recently by Steve Bannon, now the President's chief strategist.