Asked by CNN if he would subpoena for any evidence, the South Carolina Republican said, "Yes."
"All I can say is that the country needs an answer to this. The current President has accused the former President of basically wiretapping his campaign," Graham said, one day after he joined Trump for a one-on-one lunch at the White House.
Graham and Sen. Sheldon Whitehouse, a Rhode Island Democrat,
sent a letter to FBI Director James Comey and the acting deputy attorney general Wednesday, requesting any information regarding Trump's claims.
"We request that the Department of Justice provide us copies of any warrant applications and court orders — redacted as necessary to protect intelligence sources and methods that may be compromised by disclosure, and to protect any ongoing investigations — related to wiretaps of President Trump, the Trump Campaign, or Trump Tower," Graham and Whitehouse wrote.
The Trump administration has declined to provide any information about Trump's allegations since the President tweeted them last Saturday. Obama's former aides have completely denied Trump's claims, and sources told CNN Obama himself was exasperated after learning of the accusations
Ranking member of the Senate Intelligence Committee, Mark Warner, was among four senators who met with the CIA to see "raw intel" related to Russia' meddling in the US election.
"In many ways we've got even more questions now," the Virginia Democrat told reporters. "We've got more information we've got to get access to."
Asked about whether he'd seen evidence related to Trump's claims, Warner responded, "Of course we'll follow the information, we're going to follow the truth but what we have right now is ... an accusal with absolutely ... no basis in fact that anyone from the Intel community or even anybody in the staff in the White House has laid out."
Republican leaders in the Capitol, meanwhile, have largely distanced themselves from the accusations as they attempt to focus on their own internal rifts that have hobbled the effort to repeal and replace Obamacare. But Trump's accusations only added to a swirl of questions about Russia's meddling in the 2016 elections already being investigated by House and Senate lawmakers.
Sen. Susan Collins, a Maine Republican and member of the Senate Intelligence Committee, left the door open to requesting Trump's tax returns as part of their investigation -- something that could detail or dispel pervasive rumors of Trump's business ties in Russia.
"I don't know yet. It's too early to say," Collins told CNN. "What I do think that it would be helpful for us to do on the intelligence committee is to have a public hearing, where we can hear from some Russian experts."
House Intelligence Chairman Devin Nunes, who is leading a separate investigation into Russia's efforts, said Monday that he did not want to subpoena Trump's tax returns. But the top Democrat on that panel, Rep. Adam Schiff, said Democrats may seek the returns.
House investigators have set an aggressive timeline for their investigation, requesting a slew of documents from the FBI, CIA and Justice Department by March 17
and asking top current and former intelligence officials to testify in public at a March 20 hearing.
Members of the House and Senate intelligence committees, meanwhile, have been trekking to CIA headquarters to review raw intelligence.
Nunes said he wants to know why top intelligence officials changed their assessment of Russia's influence between December and January.
"What we're trying to get to the bottom of, is how did the assessment on December 5 that they gave us, how did it radically change -- with the major change being that specifically that the Russians were trying to get Donald Trump elected, and that's what we're trying to get to the bottom of," Nunes told CNN Wednesday. "It's just a major shift we need to understand and we're the oversight body."