CBS host Margaret Brennan reminded Sen. Ted Cruz (R-TX) on Sunday that there is "no evidence of fraud" that would overturn the 2020 election.

During an interview on Face the Nation, Brennan asked Cruz about reports that he had spoken to former President Donald Trump on Jan. 6.

"You knew there was no congressional authority to overturn the election," the CBS host noted. "Didn't indulging the doubters damage our democracy and our standing in the world?"

For his part, Cruz said that he was unaware of media reports claiming that he had spoken to the then-president on the same day that the U.S. Capitol was attacked.

"I didn't happen to have any conversations with President Trump on Jan. 6," Cruz insisted. "I had many conversations with him in the days, weeks and months leading up to Jan. 6. I talk to the president sometimes as often as once a week or once a day."

The senator went on to claim that he had a "responsibility" to object to the certification of electoral votes and "to review the claims of voter fraud."

"You know what you're laying out is an intellectualized argument here is not what people gathered and chanting things like Mike Pence were talking about," Brennan pointed out. "You know that."

Cruz agreed that the violence on Jan. 6 was "horrific" and should be prosecuted. But he continued to insist that Republicans could have overturned the election by appointing an electoral commission.

"Because we right now have a substantial chunk of our country that has real doubts about the integrity of the election," he opined. "And if we had had a credible electoral commission do an emergency audit, it would have enhanced faith in democracy. But instead, Democrats and a lot of the press decided to just engage in incendiary rhetoric rather than acknowledge voter fraud is real. It is a problem. And the allegations of voter fraud needed to be examined on the merits."

Brennan interrupted: "OK, Senator, there is no evidence of fraud that would really have drawn the outcome of the election into doubt. You know that."

Cruz tried to argue that voter fraud is "persistent" but Brennan ignored him and moved on to the next question.