Presumptive Republican presidential nominee Donald Trump and some vulnerable GOP lawmakers signaled Wednesday that they are open to changing the nation’s gun laws, raising the possibility that the political tide might be shifting on an issue that has sharply divided Americans for years.

This isn’t the first time a mass shooting, in this case the massacre in Orlando, Fla., that killed 49 people this week, has sparked a national cry for congressional action on gun availability. In past instances, such calls to action have been followed by intense pressure campaigns from gun rights supporters urging lawmakers to focus elsewhere.

But the debate launched this week could be different, mostly because of Trump. And it could further divide Republicans, many of whom were already distancing themselves from the presumptive nominee’s anti-Muslim rhetoric in the wake of Orlando.

Trump’s renewed focus on gun laws goes against GOP orthodoxy, which generally considers Second Amendment issues to be settled. It also complicates the Republican response to the Orlando shootings, which had focused mostly on national security and concerns about home-grown terrorism.

And Trump’s attention to the issue could strain lawmakers in tough reelection battles, including those from moderate swing states with constituents who favor tougher gun laws.

On Wednesday, Trump said he would schedule a meeting soon with the National Rifle Association to discuss proposals to ban people on certain federal watch lists from buying firearms. Trump was renewing a position he first expressed last year after a mass shooting in San Bernardino, Calif. But on Wednesday he took it to a new level, via Twitter, by calling for a meeting with the NRA.

Three Republican senators took similar stands. Rob Portman of Ohio, who is locked in a closely watched reelection battle, told reporters that he is ready to back a federal ban on weapons sales to anyone on a terrorist watch list if a compromise can be reached. Susan Collins of Maine said much the same. And Pat Toomey of Pennsylvania, who has worked on bipartisan gun-control legislation in the past and is also facing a tough reelection challenge, announced plans late Wednesday to introduce legislation after a day of talks with members of both parties as well as gun-control groups.

After the San Bernardino shooting in December, Trump told CBS’s ‘‘Face the Nation’’ that he is ‘‘very strongly into the whole thing with the Second Amendment. But if you can’t fly, and if you have got some really bad — I would certainly look at that very hard.’’

Trump’s position was buoyed this week by Senate Majority Leader Mitch McConnell, a Kentucky Republican who said he is ‘‘open’’ to keeping guns out of the hands of terrorists but not through existing proposals authored mostly by Democrats. Republicans have objected to those proposals because of the risk, they say, that innocent Americans improperly listed might be denied the right to purchase a weapon. Their counterproposals have included provisions requiring the FBI to prove that someone has engaged in terrorist activity before banning a gun purchase.

‘‘Nobody wants terrorists to have firearms,’’ McConnell told reporters on Tuesday.

The NRA expressed general support for the idea — but also made clear that a ban on sales to all people on watch lists would be unfair.