The Justice Department will “pull back” from investigations into alleged civil rights abuses by local police departments, Attorney General Jeff Sessions said Tuesday in addressing what had been a hallmark of the Obama administration.

In his first major speech as the nation’s top law-enforcement officer, Mr. Sessions told a gathering of state attorneys general that the intervention had made police less aggressive, and he vowed to crack down on violent crime as a central part of his tenure. Mr. Sessions used more measured language...