President Donald Trump stands by his accusation that the Obama administration tapped his phones during the 2016 presidential campaign, the White House has said, despite three senior legislators rejecting Trump's claim.

The Republican and Democratic leaders of the Senate Intelligence Committee said in a statement on Thursday they saw "no indications" of surveillance at Trump Tower in New York as the president claimed in Twitter posts on March 4.

"Based on the information available to us, we see no indications that Trump Tower was the subject of surveillance by any element of the United States government either before or after Election Day 2016," Republican Chairman Richard Burr and Senator Mark Warner, the committee's Democratic vice chairman, said in a statement.

The top Republican in Congress, House of Representatives Speaker Paul Ryan, on Thursday added his voice to those saying there was no sign of phone tapping.

But White House spokesman Sean Spicer forcefully defended Trump's assertion during a briefing, citing media reports that have discussed intelligence collection on possible contacts between Trump associates and Russia in the campaign.

"There is no question that there were surveillance techniques used throughout this," Spicer said.

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When pressed for further evidence, Spicer chastised the media for focusing so much attention on comments disparaging Trump's claim about surveillance.

He said reporters have not focused enough on comments from officials denying evidence of any collusion between Russia and the Trump campaign.

The Russian government has rejected an accusation by US intelligence agencies that it worked to influence the election in Trump's favour by hacking computer systems, among other methods.

Ryan said: "The point is, the intelligence committees in their continuing, widening, ongoing investigation of all things Russia, got to the bottom - at least so far - with respect to our intelligence community that - that no such wiretap existed."

Trump accused Barack Obama of tapping his phone during the late stages of the campaign, but provided no evidence.

Obama said through a spokesman that it was "simply false".

"How low has President Obama gone to tap my phones during the very sacred election process. This is Nixon/Watergate. Bad (or sick) guy!," Trump wrote.

Trump appeared to back away from his accusation of literal "wire-tapping" in a Fox News interview on Wednesday night.

"But wiretap covers a lot of different things. I think you’re going to find some very interesting items coming to the forefront over the next two weeks," Trump said.

In the briefing on Thursday, his press secretary cited unproved media reports that President Obama asked Britain's signals intelligence agency, GCHQ, to monitor Trump in order to "make sure there were no American fingerprints".

Spicer quoted at length from a Fox News report, that alleged Obama had used GCHQ to dodge US legal restrictions on monitoring US citizens.

In the Fox report - which came almost two weeks later - Andrew Napolitano claimed that "three intelligence sources have informed Fox News that President Obama went outside the chain of command" to order the tap.

"He didn't use the NSA, he didn't use the CIA, he didn't use the FBI, and he didn't use the Department of Justice," Napolitano said, adding that Obama used GCHQ.