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7 year oldSheldon Whitehouse, a Democrat, and Republican Lindsey Graham sent the letter to the FBI on Wednesday.
They requested "any warrant applications and court orders... related to wiretaps of President Trump, the Trump campaign, or Trump Tower".
Mr Trump tweeted the unsubstantiated claim over the weekend.
"Just found out that Obama had my 'wires tapped' in Trump Tower just before the victory," he posted in a series of tweets on Saturday morning.
Mr Trump was reportedly in high spirits after making the broadside on Twitter, advisers told the New York Times.
But according to the newspaper, after a round of golf, Mr Trump seemed to think he had gone too far, though still maintained his phones had been tapped.
Despite repeated requests, the White House has not supplied any evidence for the claim.
It has called on Congress to look into the allegation as part of an ongoing investigation into alleged Russian meddling in the 2016 US election.
Mr Graham and Mr Whitehouse, two senior members of the Senate Judiciary Committee, also addressed Wednesday's letter to the Department of Justice.
"Congress must get to the bottom of President Trump's recent allegation that President Obama wiretapped President Trump's phones during the 2016 election," they wrote.
Mr Graham met Mr Trump for lunch on Wednesday, telling CNN it "really was great" and the president is in a "problem-solving, deal-making mode".
But he did not mention whether he discussed the wire-tapping claims with Mr Trump.
Meanwhile, details are emerging about how Mr Obama reacted to the explosive accusations.
The former president reportedly "rolled his eyes" after learning of Mr Trump's allegations, a source close to him told NBC News.
Mr Obama reportedly thinks his successor's unfounded claims "undermine the integrity of the office", according to the source.
But he is "much more concerned" about his successor's actions on health insurance, understaffing the government, rolling back regulations and allowing mentally unstable people to buy guns with no scrutiny, the source added.
"He cares about all those things much more than what President Trump tweets at the TV each morning," the source added.
That reaction contradicted an earlier report from the Wall Street Journal on Wednesday, alleging that Mr Obama was "livid" with anger about the wire-tapping accusations.
Mr Trump reportedly called Mr Obama to thank him for the letter he left in the Oval Office, but his call was never returned, according to the newspaper.
FBI Director James Comey has reportedly rejected the allegation while James Clapper, the director of national intelligence at the time of the election, flatly denied the claim.
When pressed about the allegations, White House Press Secretary Sean Spicer told reporters on Tuesday the president has "absolutely" no regrets about making the claims.
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