The White House has asked the House and Senate intelligence committees to investigate the matter as part of their inquiries into Russia's hacking of the presidential election and possible contacts between Trump associates and Russian officials. A GCHQ spokesman called it "nonsense" and "utterly ridiculous", the BBC reported.
The British spy agency told ITV News that any suggestion it was involved in wiretapping the now president "was utterly ridiculous and should be ignored".
"I think you're going to find some very interesting items coming to the forefront over the next two weeks", Trump said.
The lowlight of Spicer's performance was a lengthy reading of press clips - largely from conservative columnist and pundits - that allegedly made the case for why Trump was right about the wiretapping.
"The president's already been very clear that he didn't mean specifically wiretapping", he said.
A spokesman for Obama has denied that he personally ordered surveillance against Trump.
Mr Trump has claimed that Trump Tower in NY was under surveillance.
Despite this, during Thursday's press briefing Sean Spicer insisted that Trump "stands by" his statements that he was under surveillance.
The administration has struggled to justify Trump's charge for more than a week, as the top Republican and Democrat on the Senate Intelligence Committee jointly stated Thursday they've seen no evidence of any surveillance of Trump Tower.
The phrasing of the statement left open the possibility that tenants or employees working in the tower may have been monitored. The department is scheduled to provide a response to the committee by Monday. That cast into concern some of the activities that happened in the 2016 election.
The senators joined a growing, bipartisan group of lawmakers who have publicly disputed Trump's accusation in the lead up to Comey's testimony. They were joined last week and again on Wednesday by House Intelligence Committee Chairman Devin Nunes, R-Calif. - leading a similar investigation in the House - who also stated that he has not seen evidence to support the president's complaint that his offices were wiretapped during the campaign.
The White House has said that Trump's initial claims, posted in a flurry of tweets earlier this month, should not be taken literally.
But the issue is unlikely to pass as quickly as some Republicans hope.
"He didn't use the NSA, he didn't use the Central Intelligence Agency, he didn't use the Federal Bureau of Investigation and he didn't use the Department of Justice, he used GCHQ". He said: "I don't believe in isolationist policy, but I also believe that a trade policy should be fair".
The U.S. National Security Agency (NSA) works closely with its counterparts in the U.K., Canada, Australia and New Zealand, under an agreement informally termed the "Five Eyes" intelligence agreement or convention.