“This is not a list that you can be certain of,” Mr. Bush told ABC. “The first impulse of Hillary Clinton and Barack Obama is to have gun control.”

Proposals to impose any restrictions on guns have been a nonstarter in Congress in recent years, despite the increasing prevalence of mass shootings. Opponents of gun control argue that gun laws will not deter people intent on committing murder, and they assert that it is safer to be armed in a dangerous world.

But not all of the Republicans seeking the White House were so certain that gun rights should apply to people who the government thinks could be plotting terrorist attacks. For candidates who have claimed that they would be the toughest against terrorists, the idea of letting homegrown radicals easily buy guns was a concern.

Gov. Chris Christie of New Jersey, who called Mr. Obama’s proposal “cynical,” allowed on Monday in an interview with The Weekly Standard that “in theory, I don’t have a huge problem” with stopping people on the no-fly list from purchasing guns.

Taking it a step further, Gov. John R. Kasich of Ohio characterized imposing gun restrictions on people on the no-fly list as an obvious measure. “Of course, it makes common sense to say that, if you’re on a terrorist watch list, you shouldn’t be able to go out and get a gun,” Mr. Kasich said over the weekend.

And Donald J. Trump, who has been leading the field in most national and state polls for months, said that he also would be open to preventing terrorism suspects from buying firearms.