WASHINGTON – The House passed a bill overhauling the National Security Agency’s heavily criticized telephone-surveillance program, in the first legislative move responding to revelations about the NSA’s spying by former government contractor Edward Snowden nearly a year ago.

Proponents said the bill marked the first substantial rollback of spy agency powers in more than 35 years, The Wall Street Journal Reported.

The bill, which passed 303-121, would restructure the way the NSA collects and searches Americans’ phone records as it investigates terrorism. Instead of collecting millions of Americans’ phone records en masse, the NSA would ask phone companies to query their databases for connections to suspicious phone numbers.

The fate of the bill, which is backed by the White House, now lies with the Senate, where it received a measured endorsement Thursday from Sen. Patrick Leahy (D., Vt.), chairman of the Senate Judiciary Committee. Senate Intelligence Committee Chairman Dianne Feinstein (D., Calif.) said she was open to considering the bill.

Leahy called the bill “an important step toward reforming our nation’s surveillance authorities,” but said he was “disappointed” the legislation didn’t include further restrictions. He said his committee will take the bill up next month.

The House bill faced last-minute opposition from lawmakers concerned that its language had been revised in a way that would expand the scope of spy-agency data searches. Critics have vowed to pursue a more restrictive version of those provisions in the Senate.

The change came in a definition of the terms used in the bill. Earlier versions of the bill would have limited searches to “a person, account, or entity.” The new version of the bill allows for searches “such as” a person, account or entity. Congressional officials said the change was sought by intelligence agencies.

Some Democrats, including several from the Silicon Valley area, objected to the bill, saying changes inserted after committee approval had weakened its protections.

“Changes were made without the knowledge of the committee members, and the result is a bill that actually will not end bulk collections, regretfully,” said Rep. Zoe Lofgren (D., Calif.).

A fellow California Democrat, Rep. Mike Honda also said he was disappointed the bill has been “so drastically weakened, adding, “It leaves open the possibility that bulk surveillance could still continue.”

House Speaker John Boehner (R., Ohio) defended the bill against criticism on Thursday, saying it put in place protections that lawmakers had sought on collection of the phone data. “There’s no access to this data without a court decision, and the standards for that decision are higher than they were,” he said.

House Republicans and the Obama administration didn’t significantly diverge over the direction of the legislation, he noted.