Former Trump Deputy Attorney General Rod Rosenstein on Wednesday offered lawmakers a limited defense of the Russia investigation he oversaw, as he came under increasing criticism from Republicans.

Mr. Rosenstein said he stood by his decision to appoint special counsel Robert Mueller to investigate Russian interference in the 2016 presidential election and any links between that effort and the Trump campaign, but said he didn’t know then of the alleged improprieties that have surfaced in recent months on aspects of the Federal Bureau of Investigation’s handling of the investigation.

“I believed at the time…and I still believe it was the right decision under the circumstances,” Mr. Rosenstein said in his most extensive comments about the investigation since leaving the Justice Department in May 2019. Asked if he would have stopped the investigation if he knew then what he knew now, Mr. Rosenstein said: “Based on what I know, no.”

The hearing comes as the Justice Department has revisited several cases that stem from that FBI investigation, dubbed Crossfire Hurricane.

The Justice Department’s watchdog in December found “serious performance failures” in how the FBI handled its requests to secretly surveil one of the subjects of the investigation, former Trump campaign foreign-policy adviser Carter Page. The report also said the FBI was justified in opening its initial investigation.

The chairman of the Senate Judiciary panel, Sen. Lindsey Graham (R, S.C.), said he had initially supported Mr. Mueller’s appointment but had come to believe the FBI’s investigation was replete with errors and driven by animus against President Trump, echoing Mr. Trump’s own criticism of the probe. “We’re going to be talking about how it got off the rails, who’s responsible for it getting off the rails, and making sure that they are punished,” Mr. Graham said.