Deputy Attorney General Rod Rosenstein defended the Justice Department’s handling of the special counsel’s still-secret report, saying Attorney General William Barr is “being as forthcoming as he can” about his process for redacting and releasing the roughly 400-page document.

In his first interview since the conclusion of the special counsel’s investigation, Mr. Rosenstein beat back suggestions that Mr. Barr is trying to mislead the public by releasing only a four-page summary of Robert Mueller’s investigation. The attorney...