Leading senators have unveiled proposed changes to the way the National Security Agency gathers U.S. records in its hunt for overseas terrorists or spying targets.

And top intelligence officials say they will cooperate with the proposed overhaul to try to win back public trust following disclosures about the NSA's extensive collection of telephone and email records of millions of Americans.

The Senate Intelligence Committee's bipartisan leadership used a hearing Thursday to promote legislation to change the Federal Intelligence Surveillance Act. The lawmakers seek to trim the NSA's authority to access and analyze U.S. phone records and provide new protections to Americans' privacy.

They also want to broaden the government's spying powers to allow monitoring of terror suspects who travel to the U.S. after being tracked overseas by the NSA.