President Donald Trump listens during a meeting on healthcare in the Roosevelt Room of the White House in Washington, Monday, March 13, 2017.
President Donald Trump listens during a meeting on healthcare in the Roosevelt Room of the White House in Washington, Monday, March 13, 2017.

The White House is continuing to stand by President Donald Trump's insistence that former President Barack Obama wiretapped his phones at Trump Tower in New York, despite a complete lack of evidence.

Spokesman Sean Spicer faced off Thursday against a roomful of reporters who wanted to know why Trump keeps insisting it is true, even after top lawmakers on the House and Senate intelligence committees say it never happened.

Spicer accused the journalists of "mischaracterizing" what happened in the Senate committee.

WATCH: Spicer on wiretapping allegations

WATCH: Spicer, CNN reporter have terse exchange over wiretapping allegations

He also accused reporters of "cherry picking" what they choose to cover, and of ignoring House Intelligence Chairman Devin Nunes, who said it was "very possible" there was surveillance of Trump.

But Nunes said he does not believe Trump's phones were tapped.

Spicer said Trump put the word "wiretap" in quotes in his original Twitter accusation. Spicer said that means there was widespread surveillance if not actual phone taps.

But the two top senators on the Senate Intelligence Committee, Republican Richard Burr and Democrat Mark Warner, said Thursday: “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.”

WATCH: Ryan says no evidence of wiretapping

Their statement followed one from House of Representatives Speaker Paul Ryan, who also dismissed the president's explosive claim March 4 that Obama ordered the eavesdropping. "We've cleared that up, that we see no evidence of that," Ryan said.

Trump, however, told Fox News late Wednesday that he "very soon" will produce evidence of Obama's actions.

Top leaders of the House Intelligence Committee said Wednesday that Trump's allegation is unfounded, but the president said his administration "will be submitting things" to the panel and that he perhaps will be speaking about his claim next week.

"You're going to find some very interesting items coming to the forefront over the next two weeks," Trump said.

Sen. Lindsey Graham, chairman of the Senate Judici
Sen. Lindsey Graham, chairman of the Senate Judiciary subcommittee on Crime and Terrorism, joined by Sen. Sheldon Whitehouse, displays a letter to FBI Director James Comey saying Congress needs to get to the bottom of charges by President Trump that his o

?Numerous congressional leaders, both opposition Democrats and Republicans, have sharply rebuked Trump's claim that Obama wiretapped Trump Tower, the skyscraper where the billionaire real estate mogul ran his campaign, and his home before winning the White House.

Trump made the wiretapping charge against his predecessor two Saturdays ago in a string of Twitter comments. One of them said: "Terrible! Just found out that Obama had my 'wires tapped' in Trump Tower just before the victory."

Obama dismissed the allegation as "simply false," and Trump since then has not substantiated his claim. Until the Fox interview, Trump dodged reporters' questions about the allegation.

Trump told Fox his Twitter comment "really covers surveillance and many other things. Nobody ever talks about the fact that (the words 'wire tapped') was in quotes, but that's a very important thing."

WATCH: Nunes denies evidence of wiretapping

On Wednesday, House Intelligence Committee Chairman Republican Devin Nunes, who has been supportive of Trump, held a news conference about Trump's wiretapping allegation.

"We don't have any evidence that took place," he said.  "I don't think there was a tapping of Trump Tower."

The committee's top Democrat, Congressman Adam Schiff, agreed, saying: "To date, I see no evidence (of Obama ordered wiretapping), no basis for that whatsoever."

WATCH: Schiff says Trump's allegations 'irresponsible'

Nunes and Schiff said they are waiting for information from the Department of Justice by next Monday about whether the agency knows of any court ordered wiretaps of Trump, but said they have learned of no such bugging in their investigation.

The congressional probe was requested by the White House after Trump made his wiretapping allegation.

The House Intelligence Committee also is looking at links between Trump campaign aides and Russian officials during the billionaire real estate mogul's long run for the White House, and in the weeks after he won the election.

Nunes said James Comey, director of the Federal Bureau of Investigation, the country's top law enforcement agency, will testify next Monday before the Intelligence Committee about the wiretapping allegation and the agency's investigation of Russian meddling in the election aimed at helping Trump win.

One key U.S. senator, Lindsey Graham of South Carolina, said, "I'm going to get to the bottom of this. Congress is going to flex its muscle."

He vowed, if need be, to subpoena the FBI to determine whether any U.S. judge issued a secret wiretapping edict that the FBI carried out.