(CNN) Rep. Adam Schiff said former White House national security adviser Susan Rice is welcome to testify before the House intelligence committee about accusations she improperly handled classified intelligence about associates of President Donald Trump.

"Whether she has pertinent testimony or not, I can't say. If she does, we'd be happy to have her come in," the committee's top Democrat told CNN's Chris Cuomo Wednesday on "New Day." "But at the same time, people that are saying that, you know, she's the 'Typhoid Mary' of national security, that's grossly irresponsible to say those kind of things, particularly people who aren't privy to any of the information."

"So it's deeply disturbing when I see that kind of accusation level," Schiff said.

Rice reportedly attempted on numerous occasions to uncover the identities of Trump's associates caught on tape incidentally during intelligence surveillance. The report quickly reopened an unsubstantiated debate on whether the Obama administration previously ordered wiretaps on Trump's phones. Rice told MSNBC Tuesday it was "absolutely false" that the administration used the intelligence for political purposes.

While Schiff said he is open to hearing Rice's testimony, he said he is not interested in attacks on her public service record.

"What I don't welcome, though, is trying to besmirch the reputation of someone who served the country very well," he said. "I don't know what it is about Susan Rice that has always drawn the conspiracy theories of that Breitbart crowd. But they're at it again and it is a disservice to someone who is a public servant."

The conservative news outlet recently reported that Sen. Mike Lee said "the unconfirmed reports that President Barack Obama's national security adviser Susan Rice unmasked the associates of President Donald Trump who were caught accidentally in surveillance operations confirmed to him the dangers of government snooping."

"Every presidential administration from FDR through Nixon, the administration in power used intelligence agencies to engage in political espionage," the Utah Republican told Cuomo Wednesday on "New Day. "Human behavior hasn't changed. Technology has changed and made a lot of this simpler. We have to be on the lookout for it."

But Lee attempted to downplay any suggestion that he told Breitbart that he believes Rice's actions were politically motivated.

"I'll tell you what I told them. I don't know what happened in this particular instance. I don't know what Susan Rice did or didn't do. That is under investigation," he said. "What I said to Breitbart and every other media outlet that asked about it, I have been expressing concerns about section 702 of (the Foreign Intelligence Surveillance Act) for the last six years."

Cuomo asked the Republican lawmaker why was he conflating potential surveillance with incidental surveillance.

"You have no reason to believe that any of those concerns are at play with Susan Rice," Cuomo said. "In fact, you have every reason to believe they were not at play with Susan Rice because as far as you or I know, we never heard of anybody wanting to leak and doing so by leaving a paper trail of making a request for the information that she got."

Lee pushed back on the suggestion that he was conflating the two.

"I have done no such thing," he told Cuomo. "For the third time on your program this morning and to reiterate something I've said every single time to reporters, I don't know what happened with Susan Rice."

"You did say it is not unreasonable to suggest it could have happened," Cuomo replied. "Now, that doesn't fly in a court of law, but it does fly in the court of public opinion."

"It seems you are saying Rice has to prove it wasn't politically motivated for me to believe it wasn't. That is not fair," he added.

Lee said he did not suggest that Rice has to prove that her actions weren't politically motivated, but said it isn't absurd to suggest that they could have been.

"That's an absolutely absurd manipulation of what I said. That is not at all what I said," he told Cuomo. "I did, in fact, say it is not absurd to suggest something like this could have happened."

"Every time I said anything like that, it has been accompanied by 'I don't know what Susan Rice did,'" Lee added. "I don't know the facts of the case. I'm sure it will be investigated."