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Washington • Sen. Mike Lee said Sunday that, to the best of his knowledge, President Donald Trump is "fully cooperating" with the probe into possible ties between Russia's meddling in the U.S. election and Trump's team, and that the firing of FBI Director James Comey hasn't hampered that investigation.

Lee, a Utah Republican who appeared on "Fox News Sunday," said he might not agree with Trump's remarks that the Russia inquiry was on his mind when he decided to fire Comey, but that doesn't mean he was trying to curtail the ongoing investigation.

"Look, that might not be the best approach to take in any given moment, but again it reflects the way he feels about the investigation," Lee told Fox's Chris Wallace, noting that Deputy FBI Director Andrew McCabe said under oath to Congress last week that there had been no White House effort to undermine the probe.

"I take him at his word," Lee said of McCabe. "And I think that indicates that this investigation is moving forward."

Asked by Wallace if Lee, as a former assistant U.S. attorney for Utah, would be concerned about the president jettisoning the FBI director in the midst of an investigation that could ensnare Trump, Lee said the action wouldn't halt the FBI from doing its job.

Wallace noted that Trump has called the investigation a hoax and a charade.

"Well, I don't think it's necessarily inconsistent to say he doesn't think there's anything there and to be willing, on the other hand, to allow the investigation to move forward," said Lee, a member of the Senate Judiciary Committee. "As far as I'm aware, he is fully cooperating and he is willing and eager to see this investigation follow itself all the way through, to wherever the facts may lead. He himself sounds confident that it's not going to lead anywhere."

Last week, Trump tweeted that Comey "better hope that there are no 'tapes' of our conversations before he starts leaking to the press!"

Some Democrats and others questioned whether that meant Trump was recording conversations at the White House; press secretary Sean Spicer declined to say if that was the case.

Lee said on "Fox News Sunday" that if there are such recordings, they will be subpoenaed and the White House would have to turn them over.

"We know that there have been instances in the past in which other presidents have made recordings of conversations that have taken place at the White House," Lee added. "And as was made clear earlier in the show, it doesn't always turn out well. It's not necessarily the best idea."

Sen. Lindsay Graham, R-S.C., agreed the tapes, if they exist, would eventually surface.

"If there are any tapes of this conversation, they need to be turned over," Graham told NBC's "Meet the Press."

On ABC's "This Week" with George Stephanopoulos, Sen. Mark Warner of Virginia, the ranking Democrat on the Senate Intelligence Committee, said the panel's own probe into any Russia-Trump connections would include asking for those recordings.

"We want to make sure those tapes are preserved, because we're going to take a look at them in Congress," Warner said.

The Democrat also said that while the law allows a president to fire an FBI director, the person in that role is appointed for a 10-year stint to avoid any political interference.

"And unfortunately, I think you have seen that political interference, because the White House, itself, switched stories midweek and said, 'Yes, the president said he was going to fire him regardless of what the deputy attorney had said, because of the Russia investigation,'" Warner said.