White House Press Secretary Sean Spicer spoke of the claims first made on US TV channel Fox News. But Trump, who rarely admits he's wrong, has been unmoved, leaving his advisers in the untenable position of defending the president without any credible evidence.
"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", the chairman and vice chairman of the committee said.
Burr and Warner are leading the Senate investigation into Russia's suspected interference in the 2016 elections to aid Trump. But the story was about intelligence agencies monitoring Russian officials - and how, through that regular surveillance, they may have discovered contacts between those officials and Trump associates.
"Top Republican in Congress, House of Representatives Speaker Paul Ryan, also agreed saying that there was no sign of a wiretap".
Trump has so far refused to fully detail what evidence he's seen to support his allegation. There was an article, I think they used that exact term.
The president's allegations are expected to dominate a March 20 House Intelligence Committee hearing with Federal Bureau of Investigation Director James Comey and National Security Agency Director Mike Rogers.
He says that when it comes to wiretapping, "At least we have something in common, perhaps".
"Judge Andrew Napolitano made the following statement, quote, 'Three intelligence sources have informed Fox News that President Obama went outside the chain of command [to spy on Trump],'" Spicer said.
Asked whether President Trump had raised the allegation with British Prime Minister Theresa May, Spicer said: "It has not been raised".
Despite this, during Thursday's press briefing Sean Spicer insisted that Trump "stands by" his statements that he was under surveillance.
The Times article that Trump cites - as his primary source - did have the words "wiretapped data" in its headline.
"The president's already been very clear that he didn't mean specifically wiretapping", he said. That was a statement made by a very talented lawyer on Fox.
There is no evidence such spying took place and GCHQ, the British electronic intelligence agency, has called the allegation "utterly ridiculous".
A spokesman for Obama has denied that he personally ordered surveillance against Trump.
The Justice Department says it delivered documents to congressional committees responding to their request for information that could shed light on Trump's Obama spying claims.
"I've been reading about things", Trump said.