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President Obama’s pledge not to back any Democrat who does not support new gun-control measures set off a new skirmish late Friday between Hillary Clinton and Senator Bernie Sanders, with Mr. Sanders facing fresh questions over his record on the issue.

Mrs. Clinton called on Mr. Sanders to admit he was wrong for having supported legislation that shields gun makers and dealers from liability lawsuits.

Mr. Sanders’s campaign manager hit back by accusing Mrs. Clinton of flip-flopping on the subject by favoring expanded gun control measures as a Senate candidate in 2000, then positioning herself alongside gun owners in opposition to Mr. Obama during their 2008 primary, before arriving at her present position favoring strict new measures.

The back-and-forth between the two leading Democrats vying to succeed Mr. Obama came after the White House stopped conspicuously short of affirming that the president would campaign for Mr. Sanders if he became the Democratic nominee.

“If Democratic voters across the country confirm that he is the Democratic nominee, then I’m confident that we’re going to spend some time here learning about his record and learning about what is on his agenda to make that decision,” Josh Earnest, the White House press secretary, said of Mr. Sanders.

A more customary response would be to say simply that the president would support whoever won the Democratic nomination.

Mr. Sanders’s mixed record on gun control has been one of his major vulnerabilities in the Democratic primary, especially as Hillary Clinton has embraced the issue of gun violence as one of the animating causes of her campaign.

In an Op-Ed article published by The New York Times on Thursday night, Mr. Obama pledged that he would not “campaign for, vote for or support any candidate, even in my own party, who does not support common-sense gun reform.”

Among other issues, Mr. Obama lamented that Congress had “guaranteed that manufacturers enjoy virtual immunity from lawsuits, which means that they can sell lethal products and rarely face consequences.”

Mr. Earnest said that the president’s mention of the immunity issue in his Op-Ed “was not any sort of secret or subtle signal to demonstrate a preference in the presidential primary.”

But the issue has provided a clear distinction between Mr. Sanders and Mrs. Clinton in the race so far.

In 2005, as a House member, Mr. Sanders voted in favor of legislation to shield gun makers and dealers from liability lawsuits. Mrs. Clinton, then a senator from New York, voted against the bill, and she has promised to seek its repeal.

On MSNBC’s “Hardball” on Friday, Mrs. Clinton asserted that Mr. Sanders “has been wrong on gun safety,” and said the issue “represents a very clear choice in a Democratic primary.”

She pointedly criticized him over his vote on the immunity legislation.

“When it really mattered, Senator Sanders voted with the gun lobby and I voted against the gun lobby,” Mrs. Clinton said. “So this is a significant difference, and it’s important that, you know, maybe it’s time for Senator Sanders to stand up and say, ‘I got this one wrong.’ But he hasn’t.”

Mr. Sanders’s campaign manager, Jeff Weaver, asserted earlier Friday that there was “about zero daylight” between the senator’s position and the president’s on gun control.

In a statement issued Friday night, Mr. Weaver portrayed Mrs. Clinton as having trimmed her sails on gun control for political expediency.

“Today she’s attacking Bernie on guns,” he said. “Eight years ago she attacked Barack Obama on guns.”

The Sanders campaign said that as a Senate candidate in New York in 2000, Mrs. Clinton favored licensing all gun buyers and establishing a registry of all handgun sales, but that, running for president in 2008, she said she no longer believed such “blanket rules” made sense at the federal level.

Also in 2008, the campaign noted, Mrs. Clinton accused Mr. Obama of being “elitist and out of touch” for making “demeaning remarks” about gun owners – prompting Mr. Obama to suggest she was acting like Annie Oakley “packin’ a six-shooter.”

“As is the case with so many issues on which she has flip-flopped, voters have to ask themselves which Hillary Clinton is asking for their vote,” Mr. Weaver said.

Mr. Sanders has repeatedly faced questions about his record on guns, and, specifically, his vote on the immunity legislation.

“If somebody has a gun and it falls into the hands of a murderer and that murderer kills somebody with the gun, do you hold the gun manufacturer responsible?” he said on CNN in July. “Not any more than you would hold a hammer company responsible if somebody beats somebody over the head with a hammer.”

But he has since backed away from his vote for the measure, at least to some extent. Asked in a debate in October if he wants to shield gun makers from lawsuits, he responded, “Of course not.” He called the 2005 legislation “a large and complicated bill” and suggested his intent was to protect gun shop owners, not manufacturers.

In an interview on CBS in December, Mr. Sanders said that he was “willing to rethink that piece of legislation and make it more effective.” But he added that “there were elements in that vote back then that did make sense.”

“If a small gun shop owner in the state of Vermont sells a product, a gun, legally to somebody else who then goes out and does something crazy, do I think that that small gun shop owner should be held liable for legally selling the product?” he asked. “No, I don’t.”