WASHINGTON — The House neared approval of legislation Wednesday to end the National Security Agency’s bulk collection of Americans’ phone records but still allow the agency to search the data on a case by case basis. Passage would set the stage for a Senate showdown just weeks before the law authorizing the program is to expire.

If the House bill becomes law, it would represent one of the most significant changes stemming from the security leaks of former NSA contractor Edward Snowden, but Senate Republicans don’t like the measure. Senate Majority Leader Mitch McConnell has introduced a separate version that would keep the program as it is, but he faces opposition from within his own party, too, and has said he is open to compromise.

President Barack Obama supports the House legislation, which is in line with a proposal he made last year.

The issue, which exploded into public two years ago, has implications for the 2016 presidential contest, with Republican candidates staking out different positions.

The revelation that the NSA had for years been secretly collecting all records of U.S. landline phone calls was among the most controversial disclosures by Snowden, a former NSA systems administrator who in 2013 leaked thousands of secret documents to journalists. The program collects the number called, along with the date, time and duration of call, but not the content or people’s names. It stores the information in an NSA database that a small number of analysts query for matches against the phone numbers of known terrorists abroad, hunting for domestic connections to plots.

Officials acknowledge the program has never foiled a terrorist attack, and some within the NSA had proposed abandoning it even before it leaked — on the grounds that its financial and privacy costs outweighed its counterterrorism benefits.

Proponents of keeping the program the way it is argue that the rise of the Islamic State group and its efforts to inspire Westerners to attack in their own countries, make it more important than ever for the NSA and FBI to have such phone records at their disposal to map potential terrorist cells when new information surfaces. And they say there is no evidence the program has ever been misused.

Under the House measure, known as the USA Freedom Act, the NSA would no longer collect and store the records, but the government still could obtain a court order to obtain such data from the phone companies, which typically store them for 18 months.

The Senate will have a short window to act before Patriot Act provisions authorizing the phone records program and other counterterrorism-related measures expire June 1. If McConnell’s bill passes to reauthorize the law with no changes, that would be seen as a crushing defeat for surveillance opponents.

On Tuesday, NSA Director Admiral Mike Rogers and FBI Director Jim Comey briefed senators on the program. Afterward, Sen. Bob Corker of Tennessee told reporters the NSA was not collecting all the data it should be. He wasn’t specific, and a spokesman declined to clarify his remarks, but he appeared to be addressing the fact that the collection does not include most mobile calls in an era when many people have stopped using landlines.

“The way it’s being implemented today, I don’t see how it’s … useful at all to the American people,” Corker said. “And I’m shocked, shocked … by the small amount of data that is even part of the program. It needs to be ramped up.”

U.S. officials have confirmed the mobile records gap, saying it stemmed from technical and policy issues that ultimately would have been addressed absent the Snowden leak. Under the House’s USA Freedom Act, they said, the NSA would expand its queries to include mobile records, creating a potentially more effective program. But they have expressed concerns about working out an arrangement with phone providers to standardize the data so the information can quickly be searched.

Those officials, not authorized to comment publicly by name, spoke only on condition of anonymity.

Sen. Rand Paul, a Kentucky Republican who is running for president, has said he would filibuster any bill that does not end bulk collection of American records by the NSA.

Jeb Bush, another potential GOP candidate, supports the collection. “I just don’t understand the debate” over the phone records program, he said in February.

Civil liberties groups are divided over whether the bill represents a significant reform. The American Civil Liberties Union says the bill needs to be stronger, and it would be better simply to let the Patriot Act provisions expire. Another prominent group, the Center for Democracy and Technology, has endorsed the measure.

The measure would not be the first major policy change in response to the Snowden leaks. Obama last year announced new measures designed to address civil liberties concerns, including requiring the government to seek a court order each time it queries the phone records database. Obama also unilaterally curbed some surveillance of foreign allies after it was revealed that the NSA had been monitoring the cellphone of German Chancellor Angela Merkel.