Virginia Sen. Mark Warner, the top Democrat on the Senate Intelligence Committee, said his committee has made "a number of referrals" to special counsel Robert Mueller's office for prosecution, and vowed to do the same for anyone who lies to congressional investigators probing Russian interference in the 2016 election.

"If you lie to Congress, we're going to go after you. We're going to make sure that gets referred," Warner said on "Face the Nation" Sunday.

On Thursday, Michael Cohen, President Trump's former personal lawyer, pleaded guilty to lying to Congress about his involvement in an effort to build a "Trump Tower" in Moscow during the 2016 campaign. In the plea agreement, Cohen admitted to lying to the Senate and House intelligence committees about the project and the extent to which then-candidate Trump and his family were involved.

Warner declined to say whether Mueller obtained transcripts of Cohen's testimony from the Senate committee in which he lied under oath. Cohen admitted to misleading investigators "out of loyalty" to Mr. Trump and to remain in line with his "political messaging." On Thursday, Mr. Trump downplayed the plea and accused his former attorney of lying to "get a reduced sentence."

Warner said Cohen's plea contradicts Mr. Trump's multiple denials during the campaign in which he said he did not have any business links to Russia. Cohen alleged the president was actively involved in the Moscow project and claimed he discussed with Mr. Trump a possible trip to Russia as a candidate in 2016.

"I do think it would have been a relevant factor, frankly, for Republican delegates to know that during that time period when [Mr. Trump] was saying only good things about Vladimir Putin as a candidate for president he was still trying to do business with that very same government," Warner said Sunday.

Warner said he did not know whether Cohen was instructed to lie to Congress, but said it was a "very relevant question that the American people need an answer to."

Warner did not specify who else has been the subject of criminal referrals, but said the committee has an "ongoing relationship" with Mueller's office. He said the committee is still probing the question of whether members of the Trump campaign colluded with Russia, which Mr. Trump has repeatedly denied.

"That is something both Chairman Burr and I are reserving judgment until we see all of the witnesses and we've got more folks to see," he said.