Sen. Lindsey Graham of South Carolina said Sunday he would continue to investigate the Justice Department and the FBI’s actions ahead of the 2016 election, if Republicans hold the Senate and he becomes chairman of the Judiciary Committee.

Mr. Graham praised the work House Judiciary Committee Chairman Bob Goodlatte, Virginia Republican, and Oversight and Government Reform Committee Chairman Trey Gowdy, South Carolina Republican, in their probe of the Trump dossier’s connection to a wiretap warrant on Trump campaign volunteer Carter Page.

The two chairman also will interview Deputy Attorney General Rod Rosenstein on Wednesday about his having signed off on the warrant, as well as reports he offered to wear a wire to record President Trump in order to use the 25th Amendment to remove him from office.

“I want the House to keep doing what they are doing and if Nancy Pelosi takes over, all this goes away,” Mr. Graham told Fox News on Sunday. “We are not going to turn our back on this. If I’m chairman, we are going to get to the bottom of this.”

Mr. Goodlatte, who is retiring, said the Justice Department’s inspector general is also an option to continue the probe into the conduct surrounding the 2016 election if Democrats were to take the House and not continue his committee’s investigation.

“This matter is not going away based on the outcome of this election,” Mr. Goodlatte told Fox News.

Mr. Goodlatte, Mr. Gowdy and the ranking members of their respective committees — Democratic Reps. Jerry Nadler of New York and Elijah Cummings of Maryland — will conduct a closed-door classified meeting with Mr. Rosenstein. It will be transcribed so other members of Congress will get to review the interview.

“There is no limitation on the scope on these questions,” Mr. Goodlatte said.

He also said they’re interested in whether the FBI withheld mitigating evidence, suggesting there was no collusion between Russia and the Trump campaign, from the Foreign Intelligence Surveillance Court when the bureau asked for the warrant.

After November’s midterm elections, Mr. Goodlatte’s committee will publish an interim report on the findings.

Mr. Graham said if he’s chairman of the SenateJudiciary Committee, he would dig into Glenn Simpson and his firm’s work on the dossier, plus the connections between one of Mr. Simpson’s employees and her husband who worked in the Justice Department.

“I want you to know as much as you can know about how it got so off the rails. I want you to know as much as you can know FBI agents colluding with the Department of Justice to undercut Trump and to help Clinton,” Mr. Graham said.