AUSTIN, Texas — A day after President Trump’s former personal attorney Michael Cohen pleaded guilty to lying to Congress, the head of the Senate Intelligence Committee warned that anyone else who lies to lawmakers will face a similar fate, and he said that the committee has worked with special prosecutor Robert Mueller and has made multiple referrals for criminal prosecutions.

Sen Richard Burr, North Carolina Republican, told an audience at the University of Texas that Cohen’s guilty plea was just one instance of the committee learning it had been lied to, and subsequently giving that information to Mr. Mueller and his team.

“It’s a loud message to everybody that’s interviewed by our committee. … If you lie to us, we’re going to go after you,” Mr. Burr said during a candid question-and-answer session at the annual Texas National Security Forum.

Cohen pleaded guilty Thursday and said in court documents that the president’s business empire was trying to secure a Trump organization deal with Russia during the middle of the 2016 presidential campaign. Cohen previously had denied any such business dealings during the campaign.

The president’s former lawyer and “fixer” also pleaded guilty earlier this year to making illegal campaign contributions for facilitating payouts to porn star Stormy Daniels and Playboy model Karen McDougal.

Separate from the Mueller probe, which is investigating allegations of collusion between the Russia and members of the Trump campaign, Mr. Burr and Virginia Democratic Sen. Mark Warner have been conducting their own probe into Russian interference in the 2016 election. Mr. Burr stressed that their investigation, unlike Mr. Mueller‘s, isn’t centered on finding criminal wrongdoing and issuing indictments.

But he said the committee has on more than one occasion recommended prosecutions based on their interviews.

“We continually go back and look at the testimony we’ve been given, and we weigh it against any new information that might be out there that either a reporter has been able to [get] in a comment from an individual,” he said. “We have shared, when permission has been given by those we interview, interview notes with the Department of Justice and specifically with the special prosecutor.”

“We have made referrals to the special prosecutor for prosecution,” he continued. “In a lot of cases, those might be tied to lying to us.”

The Senate probe has been ongoing for nearly two years, and both Mr. Burr and Mr. Warner said Friday that much work remains to be done.