Vice President Biden said Thursday he sees an emerging consensus around “universal background checks” for all gun buyers and a ban on high-capacity ammunition magazines as he completes the Obama administration’s broad study of ways to curb the nation’s gun violence.

But the National Rifle Association, a participant in an afternoon meeting with Biden, strongly rejected what it called “an agenda to attack the Second Amendment” and indicated it would have nothing more to do with the vice president’s task force on gun laws.

The consensus Biden described is among gun-control advocates and law enforcement officials with whom he has been meeting for the past week. The gun industry has long opposed such restrictions, including background checks on private sales of firearms.

Biden, who said he would present his working group’s policy recommendations to President Obama by Tuesday, suggested that universal background checks and a high-capacity magazine ban would be part of the administration’s agenda.

Biden made the remarks as he opened a meeting with hunters and sportsmen, one of a series Thursday that also included a gathering with gun owners’ groups, notably the NRA.

Majority sees Connecticut shooting as societal problem

Biden was tasked by Obama with leading an interagency working group on gun violence in the wake of last month’s elementary school shooting in Newtown, Conn., that killed 20 small children and six educators.

Biden said that, going into Thursday’s meetings, the group has heard repeatedly about the need to strengthen background checks to keep guns out of the hands of criminals and the mentally ill. He said proposals would go beyond closing a loophole that exempts some private firearms sales, such as at gun shows, from background checks.

“There is an emerging set of recommendations — not coming from me but coming from the groups we’ve met,” Biden said. “There is a surprising, so far, a surprising recurrence of suggestions that we have universal background checks.”

These recommendations were not only about “closing the gun show loophole,” he said, “but total universal background checks, including private sales.” He said the focus would be on how to “strengthen those background checks.”

Biden also mentioned strengthening the ability of federal agencies to conduct research about gun violence. He drew a comparison between current limits on federal gathering of data about gun violence and 1970s-era restrictions on federal research into the causes of traffic fatalities. Biden stressed a need for the government to collect information about “what kind of weapons are used most to kill people” and “what kind of weapons are trafficked weapons.”

Biden’s comments came an hour before he was scheduled to meet with a senior representative of the NRA, the powerful gun rights group that has long opposed any additional restrictions on gun ownership or ammunition purchases.

In a statement after that meeting, the Fairfax-based NRA said it attended the session to “discuss how to keep our children safe” and to “have a meaningful conversation about school safety, mental health issues, the marketing of violence to our kids and the collapse of federal prosecutions of violent criminals.”

It added: “We were disappointed with how little this meeting had to do with keeping our children safe and how much it had to do with an agenda to attack the Second Amendment.” It charged that Biden’s task force “spent most of its time on proposed restrictions on lawful firearms owners” and accused the Obama administration of “pushing failed solutions to our nation’s most pressing problems.”

“We will not allow law-abiding gun owners to be blamed for the acts of criminals and madmen,” the NRA said. “Instead, we will now take our commitment and meaningful contributions to members of Congress of both parties who are interested in having an honest conversation about what works — and what does not.”

The Biden group is finishing its discussions with an array of interest groups. Thursday’s meetings conclude with an evening session with representatives of the entertainment and video gaming industries. Attorney General Eric H. Holder Jr. also is meeting separately Thursday with major gun retailers, including Wal-Mart.

On Wednesday, Biden met with gun violence victims and gun safety organizations. He also held conference calls with governors and other state and local elected officials of both parties from across the country.

During Wednesday’s meeting with victims’ groups, Biden vowed urgent action and said the administration would consider “executive actions” that do not require an act of Congress.

“This is a problem that requires immediate attention,” Biden said Wednesday. “The president and I are determined to take action.... I want to make clear that we’re not going to get caught up in the notion that, unless we can do everything, we’re going to do nothing.”

As he opened Thursday’s meeting with groups representing hunters and sportsmen, the vice president said he had already heard “a good deal of talk about gun safety,” even among former Senate colleagues “opposed to any restrictions on gun ownership.”

“I’ve never quite heard as much talk about the need to do something about high-capacity magazines as I’ve heard spontaneously from every group that I’ve met with so far,” Biden said.

Biden described himself as “an owner of shotguns,” adding: “I’m no great hunter. It’s mostly skeet shooting for me.”

He said he was still hoping to have a conference call with gun manufacturers.

“There has got to be some common ground, to not solve every problem but diminish the probability” of future mass shootings, he said. “That’s what this is all about. There are no conclusions I have reached.”

Referring to the Newtown slayings, he said: “There is nothing that has pricked the consciousness of the American people” as much as the image of “little 6-year-olds riddled ... with bullet holes” in their classrooms.

The “stakeholders” at Thursday’s first meeting sat around a large polished wooden table at the Eisenhower Executive Office Building next to the White House. They were joined by several administration officials, including Holder, Agriculture Secretary Tom Vilsack, Transportation Secretary Ray LaHood and Interior Secretary Ken Salazar.

Sari Horwitz contributed to this report.