Backers touted the bill as the first major restriction imposed on government surveillance since the late 1970s and said if it becomes law, the National Security Agency will no longer be able to collect and query most Americans’ phone records.

“The NSA might still be watching us, but now we can watch them,” said Rep. F. James Sensenbrenner Jr., Wisconsin Republican and the author of the original Patriot Act, which he said the government abused in order to start the mass snooping.

The 303-121 vote could have been more forceful had the administration not pushed for changes that watered down the bill over the past week, creating confusion about exactly what kind of snooping the NSA will be allowed to do.

The House acted almost a year after former government contractor Edward Snowden leaked details of the NSA’s phone snooping program. That leak ignited a feverish debate about the extent of government data collection.

Under the phone program, the NSA collected the numbers and durations of every phone call made inside the U.S. The content was not collected, but the agency stored the data for five years and, when it suspected a link to terrorism connected to a certain phone number, would query the data to see whom that number had called, whom those connected numbers had called and so forth — out to three “hops” away from the original number.

Intelligence agencies fiercely defended the programs as vital to national security and respectful of Americans’ privacy. Officials said the data collection had been approved by a court and that select members of Congress had been told about it.

After the data collection was revealed, the backlash from the public, and from members of Congress not privy to the program’s existence, was intense.

The vote Thursday was a first but major step toward officially ending the program. The Senate will have to approve the bill before it goes to President Obama for his signature.

The legislation also tries to prevent any request for bulk data. It changes the Patriot Act and seeks to make clear that the administration cannot use the Foreign Intelligence Surveillance Act or presidential executive orders to try to restart the programs.

Mr. Obama, who for most of his administration approved and oversaw the NSA’s bulk collection, has changed his stance. In a statement issued Wednesday, the White House said Mr. Obama “strongly supports” the bill curbing presidential powers.

“The bill ensures our intelligence and law enforcement professionals have the authorities they need to protect the nation, while further ensuring that individuals’ privacy is appropriately protected when these authorities are employed,” the White House Office of Management and Budget said.

The White House did manage to dilute the bill to the point where a number of civil liberties groups withdrew their support.

As originally written, the bill would have installed an independent advocate on the secret court that approves surveillance programs. The rewritten bill excluded that provision.

The most controversial change was selection criteria the NSA can use for queries that are still allowed.

Rep. Zoe Lofgren, a California Democrat who supported an earlier version but voted against the bill Thursday, said she couldn’t stomach those changes.

Given the intelligence community’s history, she said, she was not prepared to trust it.

“Our job is not to trust, but to codify,” she said.

She joined 69 other Democrats and 51 Republicans in opposing the bill. Many of them said they wished they had the chance to vote on the original version.

Some senators said they will try to push the original version through the upper chamber later this year.

“The NSA has shown it will seize upon any ‘wiggle room’ in the law, and there is plenty of wiggle room in the House-passed legislation,” said Sen. Mark Udall, Colorado Democrat.