Mike Lee of Utah told the "Fox News Sunday" program it was "inevitable" that they would be subpoenaed and the White House would have to release them.
With controversy roiling the White House, Trump spent part of Sunday at his private golf course in Northern Virginia.
He noted the intelligence community's joint assessment declaring Russian Federation had interfered in the 2016 election did not contain any reporting about political collusion.
When Trump did tell his staffers of Comey's firing, the news leaked to the press before Trump's letter firing Comey could arrive at the FBI's Washington, D.C. office.
Trump and Comey had a private dinner in the White House on January 27 in which a source close to Comey said the President asked the Federal Bureau of Investigation director to pledge his loyalty, which Comey, who reportedly was taken aback by the request, refused to do.
The next director will immediately be confronted with oversight of an FBI investigation into possible coordination between Russian Federation and the Trump campaign, an inquiry the bureau's acting head, Andrew McCabe, has called "highly significant".
Trump shared highly classified info with visiting Russian officials
Reporters started gathering in the hallway outside Press Secretary Sean Spicer's office right after the Post story broke. Senate Minority Leader Chuck Schumer also urged the Trump administration to give any tapes to Congress.
Republican leaders in the Senate have rebuffed calls for a special prosecutor, saying it would interfere with ongoing congressional probes. An NBC News-Wall Street Journal poll found that just 29 percent of Americans said they approve of the decision; 38 percent said they disapprove.
Democrats are demanding appointment of a special prosecutor to investigate Russia's involvement in the 2016 election and ties to Trump's campaign, and have discussed trying to slow down the confirmation process or other business of the Senate as a way of drawing attention to the demand.
"We have got to make sure that these tapes, if they exist, don't mysteriously disappear", Warner said.
Graham said there may come a time when a special prosecutor is needed but not now.
While notable, Schumer's threat may be a bit toothless: Republicans have 52 seats in the Senate, and a rules changes made in 2013 by Democrats means that whomever Trump nominates only requires a simple majority vote to be confirmed.
"It's not a criminal investigation". John Cornyn of Texas, New York Appeals Court Judge Michael Garcia and former Assistant Attorney General Alice Fisher, according to a White House official. "I see no need for a special commission yet", he said. Privately, Democrats have expressed doubt that Garland would even consent to an interview for the job.
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