WASHINGTON — Facing a Monday deadline, the Justice Department asked lawmakers for more time to provide evidence backing up President Trump’s assertion that his predecessor wiretapped his New York skyscraper during the election.

The request came as the White House appeared to soften Trump’s explosive allegation.

The House intelligence committee said it would give the Justice Department one more week until March 20 to comply with the evidence request. That’s the date of the committee’s first open hearing on the investigation into Russia’s interference in the 2016 election and possible contacts between Trump associates and Russia.

Jack Langer, a spokesman for the committee’s Republican chairman, Representative Devin Nunes, Republican of California, said that if the Justice Department doesn’t meet the new deadline, the panel might use its subpoena power to gather information.

Trump’s assertions have put his administration in a bind. Current and former administration officials have been unable to provide any evidence of the Obama administration wiretapping Trump Tower, yet the president’s aides have been reluctant to publicly contradict their boss.

White House spokesman Sean Spicer tried to clarify Trump’s comments Monday, saying the president wasn’t using the word wiretapping literally, noting that Trump had put the term in quotation marks.

‘‘The president used the word wiretap in quotes to mean broadly surveillance and other activities,’’ Spicer said. He also suggested Trump wasn’t accusing former president Obama specifically, but instead referring to the actions of the Obama administration.

Trump himself has not commented on the matter since his March 4 tweets, in which he said he had ‘‘just found out that Obama had my ‘wires tapped’ in Trump Tower just before the victory.’’

He also wrote: ‘‘Is it legal for a sitting President to be ‘wire tapping’ a race for president?’’

In two other tweets, Trump described Obama tapping his phones, but did not put the phrases in quotation marks.

The president’s accusations against Obama came amid numerous political questions surrounding his associates’ possible ties to Russia.

The FBI is investigating Trump associates’ contacts with Russia during the election, as are House and Senate intelligence committees.

The White House has asked those committees to also investigate Trump’s unverified wiretapping allegations against Obama. The House committee has turned the matter back on the Trump administration, setting the Monday deadline for the Justice Department to provide evidence.

In a response Monday evening, the Justice Department said it needed extra time to ‘‘review the request in compliance with the governing legal authorities and to determine what if any responsive documents may exist.’’

Other congressional committees are also pushing the administration to clarify Trump’s claims.

Senators Lindsey Graham, Republican of South Carolina, and Sheldon Whitehouse, Democrat of Rhode Island, asked Acting Deputy Attorney General Dana Boente and FBI Director James Comey to produce the paper trail created when the Justice Department’s criminal division secures warrants for wiretaps.

The senators, who head the Senate Judiciary Committee’s crime and terrorism subcommittee, are seeking warrant applications and court orders, which they said can be scrubbed to protect secret intelligence sources and methods.

Trump’s critics have slammed the president for making the wiretapping claim on his Twitter account without evidence. Wiretapping a US citizen would require special permission from a court, and Trump as president would have the ability to declassify that information.

Comey has privately urged the Justice Department to dispute Trump’s claim but has not come forward to do so himself. James Clapper, who was Obama’s director of national intelligence, has said that nothing matching Trump’s claims had taken place.

White House counselor Kellyanne Conway sidestepped questions about the lack of proof Monday, saying she was ‘‘not in the job of having evidence.’’

‘‘That’s what investigations are for,’’ Conway told CNN’s ‘‘New Day.’’

In a separate development Monday, Trump signed an order aimed at streamlining the executive branch.

He said the order requires the examination of every federal department and agency ‘‘to see where money is being wasted, how services can be improved, and whether programs are truly serving American citizens.’’

He said the Office of Management and Budget will oversee the evaluation, working with experts inside and outside the government to develop a reorganizing and consolidation plan.