US President Donald Trump has been urged to provide evidence to back his allegation that his predecessor, Barack Obama, ordered his phones to be tapped during the election campaign.
Republican Senator Ben Sasse said Mr Trump's comments were "serious" and he should explain the alleged wire-tapping and how he came to know about it.
The Republican president has supplied no details to back his claim.
Mr Obama never "ordered surveillance of any US citizen", his spokesman said.
Mr Trump's tweets follow allegations made by conservative radio host Mark Levin, including that the Obama administration "sought, and eventually obtained, authorisation to eavesdrop" on the Trump campaign last year.
Other media reports had previously suggested the FBI had sought a warrant from the foreign intelligence surveillance court (Fisa) in order to monitor members of the Trump team suspected of irregular contacts with Russian officials.
The warrant was first turned down but then reportedly approved in October, though there has been no official confirmation.
Under Fisa, wire-tapping can only be approved if there is probable cause to believe that the target of the surveillance is an agent of a foreign power. Mr Obama could not lawfully have ordered such a warrant.
Mr Trump, who has been facing intense scrutiny over alleged Russian interference in support of his election campaign, made the allegation in a series of tweets on Saturday.
Writing from his weekend home in Florida, he called the alleged tapping "Nixon/Watergate", referring to the most notorious political scandal of 1972, which led to the downfall of President Richard Nixon after a web of political spying, sabotage and bribery was exposed by the media.
The spokesman for Mr Obama, Kevin Lewis, said the accusation was "simply false".
A "cardinal rule of the Obama Administration was that no White House official ever interfered with any independent investigation led by the Department of Justice", he said.
The statement left open the possibility that a judicial investigation had been taking place.
Earlier Ben Rhodes, who was Mr Obama's foreign policy adviser and speechwriter, also addressed Mr Trump's claims in a tweet, saying: "No President can order a wire-tap. Those restrictions were put in place to protect citizens from people like you."
Partisan maelstrom: By Anthony Zurcher, BBC News, Washington
As the Trump administration continues to be bedevilled by a drip-drip of revelations about ties to Russian officials during and after last year's election, the president has seemingly settled on the identity of the malevolent figure behind the turmoil.
It was the former president, Mr Trump asserts, who is guilty of meddling in the 2016 campaign, not Russia. Mr Obama, he says, is the one whose deeds merit investigation.
The president's early morning tweets follow an interview on Tuesday in which he accused Mr Obama and "his people" of orchestrating recent political protests across the US and of being behind the government leaks that have embarrassed the White House.
There is scant evidence supporting these allegations, but charges like these fit a pattern. Mr Trump is at his sharpest when pushing back against perceived antagonists, such as Republican primary opponents like Jeb Bush, establishment conservatives who resisted his nomination or Hillary Clinton in the election.
Now Mr Trump is returning to his favourite political foil - a necessity given the current Democratic power vacuum in Washington. It could mark the beginning of a massive water-muddying effort in which any forthcoming investigatory revelations are swept up in a growing partisan maelstrom.
In other developments:
- ABC News quoted senior White House sources as saying President Trump had gone "ballistic" at an Oval Office meeting on Friday, in particular at the decision of Attorney General Jeff Sessions to remove himself from an investigation into alleged Russian interference in the election
- Politico and CNN report that Mr Trump will sign as early as Monday a new executive order imposing a travel ban on people from some Muslim-majority nations. The first was halted in the courts
- Trump supporters have held scores of rallies in locations across the country, ranging from several dozen people to the low hundreds, under the banner of the Spirit of America
Some Democrats have suggested Mr Trump's latest tweets are an attempt to focus attention away from the Russian affair.
House Democratic Leader Nancy Pelosi said: "The Deflector-in-Chief is at it again."