The senator who introduced hotly debated legislation intended to shut down pirate websites said Thursday he is backing away from one of the most controversial parts of the bill, amid criticism from Web companies, human rights groups and Internet engineers.

Sen. Patrick Leahy, a Vermont Democrat, said he would recommend that "more study" be given to a provision in the bill that would give the U.S. attorney general new authority to seek court orders compelling Internet service providers to block the sites' domain names or Web...