Rep. Jerrold Nadler (D-N.Y.) on Sunday said the House would investigate Supreme Court nominee Brett Kavanaugh if he's confirmed to the court and the Democrats take back the majority.

“We would have to investigate any credible allegations certainly of perjury and other things that haven’t properly been looked into before," Nadler said on ABC's "This Week."

Rep. Jerrold Nadler says if Brett Kavanaugh "is on the Supreme Court and the Senate hasn't investigated, then the House would have to" investigate "any credible allegation" of perjury and "things that haven't been properly looked into" https://t.co/HgLvOGZf0Y #ThisWeek pic.twitter.com/9RezesuZph — This Week (@ThisWeekABC) September 30, 2018

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He left open the possibility that the Senate and FBI do an adequate job investigating Kavanaugh so the House wouldn't need to step in.

"If he is on the Supreme Court and the Senate hasn’t investigated, then the House will have to," he said. Nadler is likely the next chairman of the House Judiciary Committee if the Democrats retake the House in November's elections.

Nadler said it would be "a real problem" if the FBI's investigation into Kavanaugh isn't thorough and that he hopes Sen. Jeff Flake Jeffrey (Jeff) Lane FlakeHow fast population growth made Arizona a swing state Jeff Flake: Republicans 'should hold the same position' on SCOTUS vacancy as 2016 Republican former Michigan governor says he's voting for Biden MORE (R-Ariz.), who called for the investigation, won't vote for Kavanaugh without a "proper investigation."

"I would hope that Sen. Flake and others would make clear that they will not vote for the nominee unless there is a free hand for proper investigation of these very serious allegations of sexual assault," he said.

"We cannot have a justice on the Supreme Court for the next several decades … who has been credibly accused of sexual assaults," Nadler added.

President Trump on Friday asked the FBI to conduct a "limited" investigation into sexual misconduct accusations made against Kavanaugh.

Christine Blasey Ford has accused Kavanaugh of sexually assaulting her at a high school party in the 1980s. Kavanaugh has strongly denied those allegations, including during testimony Thursday in front of the Senate Judiciary Committee.

Two other women, Deborah Ramirez and Julie Swetnick, have also publicly accused Kavanaugh of sexual misconduct since last week. Kavanaugh has also denied those accusations.