The former deputy attorney general Rod J. Rosenstein defended during congressional testimony on Wednesday his decision to appoint a special counsel for the Trump-Russia investigation, as Republican allies of President Trump sought to keep a skeptical spotlight on the inquiry heading into the November election.

“I still believe it was the right decision under the circumstances,” Mr. Rosenstein said to the Senate Judiciary Committee about appointing Robert S. Mueller III as special counsel. “I recognize that people can criticize me for them. That’s the consequence of being in these jobs, you make decisions and people criticize you for them, but I believed it was the right decision at the time.”

But Mr. Rosenstein also said that he would not have signed an application in June 2017 to renew a court wiretap order targeting Carter Page, a former Trump campaign adviser, if he had known at the time that it contained factual errors and omissions, as an inspector general found. Still, Mr. Rosenstein blamed the F.B.I. for the problems.

The chairman of the Judiciary Committee, Senator Lindsey Graham of South Carolina, has made clear that he intends to try to keep a focus in the coming months on the investigators who sought to understand the scope of Russia’s election interference and ties to Trump campaign associates.