At least two Republican senators have signaled that they may reconsider their opposition to ­expanded national background checks for gun purchases, aides said Monday, suggesting that the push for stricter gun laws could return as a top issue in Washington in the coming weeks.

The gun debate appeared to be largely abandoned on Capitol Hill following a resounding defeat in the Senate last month. But a handful of lawmakers are showing a new eagerness to engage on the issue after gun-control groups launched campaigns against senators in both parties who voted against the background check proposal.

Capitol Hill aides Monday declined to identify the two Republicans who have approached Democrats about restarting the debate. But Sens. Johnny Isakson (R-Ga.) and Jeff Flake (R-Ariz.) signaled through their spokesmen that they would be open to debating the background-check proposal again if Democrats make significant changes.

Meanwhile, aides to Sen. Kelly Ayotte (R-N.H.), who voted against the background check plan, disputed a new barrage of TV ads critical of her vote and said she remains opposed to the current bipartisan background check proposal.

Senate aides and activists pushing for stricter gun laws say there are probably two windows of opportunity for the Senate to return to gun legislation: this month after consideration of an Internet taxation bill, or this summer after wavering senators have had enough time to reconsider their position.

But key to the issue’s success would be a new groundswell of support for stricter gun laws among the general public, according to legislative aides and activists. Supportive lawmakers are waiting to see whether a new public campaign by gun-control groups and the White House will put enough pressure on senators who voted no to reconsider.

Advocates are trying to “make the pain of the vote so biting and so lasting that it is not politically sustainable,” said Mark Glaze, director of Mayors Against Illegal Guns, the group financed by New York Mayor Michael R. Bloomberg (I).

“The terrain has shifted under senators’ feet and I don’t think they’ve realized it yet,” Glaze said.

At the White House, Vice President Biden met Monday afternoon with religious leaders in part of a series of recent meetings designed to keep public pressure on lawmakers to expand background checks.

“We remain optimistic, the president does, that when it comes to background checks, that this will happen,” White House press secretary Jay Carney told reporters Monday. “We can’t say precisely when that legislation will pass, but we and the president remain convinced that it will because the American people have stated so clearly that it is a sensible thing to do.”

Conversations among senators picked up during last week’s congressional recess, with Sen. Joe Manchin III (D-W.Va.), the chief architect of the bipartisan deal, once again taking the lead, according to aides. Manchin and Sen. Patrick J. Toomey (R-Pa.) brokered the deal that would have expanded the background-check system to include most commercial firearms sales while exempting private exchanges between family members and friends.

Senate Majority Leader Harry M. Reid (D-Nev.) said in an interview with the Las Vegas Review-Journal that Manchin had called him recently to say he believed there were now more votes in support of the plan.

Bloomberg’s group began airing a new television advertisement in New Hampshire on Monday attacking Ayotte’s vote against the background-check proposal. A group founded by former congresswoman Gabrielle Giffords (D-Ariz.), who was wounded in an assassination attempt in 2011, began airing similar ads against Ayotte last week.

Ayotte spokesman Jeff Grappone called the new ads “completely false” and said that the senator voted for an alternative GOP plan to fix the background check system and strengthen mental health programs. As for Reid’s comments, Grappone said the Senate leader “doesn’t speak for Senator Ayotte.”

Lauren Culbertson, a spokeswoman for Isakson, said the senator from Georgia is open to further conversations about expanding background checks, but only if the current proposal is “significantly reworked.” In an e-mail, Culbertson said that Isakson “has major concerns with its potential impact on private sales and on privacy issues.”

Flake acknowledged on Facebook last week that his approval ratings have dropped because of his vote on the background-check proposal. His spokeswoman, Genevieve Rozansky, said in an e-mail Monday that the senator “has said all along that background checks need to be strengthened, particularly with regard to the mentally ill. So he is hopeful that changes will be made to Manchin-Toomey, or another proposal, that address his concerns regarding private sales, and that a bill will be brought back to the floor.”

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