WASHINGTON — Republican lawmakers opened the door on Tuesday to a national debate about gun control following the Connecticut school massacre, a small sign of easing in Washington’s reluctance to seriously consider new federal weapons restrictions.

Republican members of the House of Representatives, where the party holds a majority of seats, discussed the killings in their weekly closed-door conference meeting and said afterward there was more willingness now to talk about regulating weapons.

“You are going to have some people who never, never go there,” Representative Steve LaTourette, an Ohio Republican, told reporters, referring to a small number of Republicans who will not countenance any talk of gun regulation.

“But yes, I think most Republicans are willing to have a very, very serious conversation about what this means and taking a second look at what the Second Amendment (guaranteeing the right to bear arms) means in the 21st century,” he said.

Republicans are traditionally strong gun-rights advocates and receive far more campaign donations than Democrats from the powerful National Rifle Association gun lobby, which has opposed previous attempts at weapons controls.

The NRA was largely silent for the first few days after the shooting rampage at the Newtown, Connecticut, grade school in which 26 people, including 20 young children, were slain.

But the group issued a statement on Tuesday saying it had not commented out of respect for the families and to allow time for mourning and an investigation. “The NRA is prepared to offer meaningful contributions to help make sure this never happens again,” it said.

Momentum is growing in Congress for some sort of action, although the substance remains unclear.

Some Democratic gun-rights advocates, including Senator Joe Manchin of West Virginia, said on Monday they would now be open to more regulation of military-style rifles like the one used in Newtown.

On Tuesday, the White House spelled out some gun control measures and threw support behind California Democratic Senator Dianne Feinstein’s effort to craft legislation to reinstate an assault weapons ban. White House spokesman Jay Carney also said President Barack Obama would back any law to close a loophole related to gun-show sales.

Senator Frank Lautenberg, a New Jersey Democrat, called on the Senate on Tuesday to immediately pass his legislation to ban high-capacity ammunition magazines, which were used in the attacks in Connecticut as well as mass shootings in Aurora, Colorado; Oak Creek, Wisconsin; Tucson, Arizona, and at Virginia Tech, among others.

But any legislation would likely wait until 2013, after negotiations on how to address the “fiscal cliff” of spending cuts and tax hikes due to kick in at the beginning of the year.

Still, it is notable that some Republicans may be reconsidering their positions.

Representative Jack Kingston said the meeting of fellow House Republicans on Tuesday had focused heavily on the link between mental illness and mass shootings in the United States.

“Mental health is a huge part of it. No rational person squeezes the trigger in the face of a 6-year-old,” the Georgia congressman told Reuters.

However, he said the dialogue had changed. “There may be more support of discussion at this point among the pro-gun Democrats and Republicans,” Kingston said.

U.S. lawmakers have not approved a major new federal gun law since 1994, and a ban on assault weapons expired in 2004.

Not looking to government

Even as they expressed sorrow over the killings, some Republicans said they did not think an assault weapons ban — or any government action — was the answer, noting that Connecticut is a state with relatively tough gun laws.

“I just don’t know what government can do to fix this,” South Carolina Republican Senator Lindsey Graham told reporters. “I don’t think that (an assault weapons ban) fixes the problem, because you’ve got 24 million guns out there already.”

He said he thought it would make sense to create a commission to look at the broader issue of violence in the United States.

There is also no guarantee of how much Democratic support a measure would get, despite optimism from California Representative Nancy Pelosi, the top Democrat in the House, who said on MSNBC prospects for gun control were better than they had been in years.

Nevada Democrat Harry Reid, the Senate majority leader, has been less committal. In 2004, he voted against the extension of the weapons ban, and the measure died.

On Tuesday, Reid said “every idea” should be on the table for discussing how to keep children safe, but he declined to speak specifically about any gun control measure.

“We must engage in a thoughtful debate about how to change laws and culture that allow violence,” he told reporters at the Capitol.

Senator Susan Collins, a moderate Republican from Maine, said she was not sure whether members of her party would be open to restricting the sale of high-capacity ammunition clips or a ban on assault weapons.

“The conversations that I’ve had with my Republican colleagues … and indeed my Democratic colleagues, have really not focused on policy changes at this point,” she said. “It has focused on the horrible tragedy that has stunned and shocked all of us.”