WASHINGTON — The Justice Department’s internal watchdog intends to complete by May or June his investigation into aspects of the Russia inquiry, including whether law enforcement officials abused their powers in surveilling a former Trump campaign aide, Attorney General William P. Barr told lawmakers on Tuesday.

The department’s inspector general, Michael E. Horowitz, has been examining how law enforcement officials obtained a warrant in October 2016 to wiretap Carter Page, a former foreign policy adviser to the Trump campaign with links to Russia. Mr. Horowitz’s investigators have also asked witnesses about informants that the F.B.I. turned to in the early stages of the investigation, according to people familiar with his inquiry.

“The office of the inspector general has a pending investigation of the FISA process in the Russia investigation,” Mr. Barr said in testimony before a House appropriations subcommittee, using shorthand for the Foreign Intelligence Surveillance Act. “I expect that will be complete in probably May or June, I am told. So hopefully we’ll have some answers from Inspector General Horowitz on the issue of the FISA warrants.”

A spokesman for Mr. Horowitz declined to comment on the timing of the expected report. But the inspector general has previously confirmed that he was looking into the early stages of the Russia inquiry, including wiretap applications, informants and whether any political bias against Mr. Trump influenced investigative decisions.