Representative Michael McCaul, Republican of Texas and the chairman of the House Homeland Security Committee, said Monday that the F.B.I. should have the ability to interview people like Mr. Mateen who had been terrorism suspects and to obtain “full access” to their records as part of a gun-purchase application — an idea at odds with the National Rifle Association’s position on the issue.
“If, indeed, these were terrorism leads that opened up, I think the F.B.I. should have access to interview him, as they did on multiple occasions” during two earlier investigations, Mr. McCaul said on CNN.
“I don’t think that would preclude them from interviewing him,” Mr. McCaul said. “Let’s not forget what the real threat is. Many of these terrorism cases involve stolen firearms, AK-47s. An outright ban is not going to solve the problem. But I do think that the F.B.I. should have full access to any potential terrorist in this country that is looking to purchasing a firearm.”
Also on Monday, the nonprofit Brady Campaign to Prevent Gun Violence renewed its call to impose tougher restrictions on the sales of high-powered rifles and other firearms.
“We can’t allow it anymore,” Dan Gross, the organization’s president, told reporters. “We can’t let it be so easy for people to get guns. We can do so much better than this.”
He acknowledged the gun industry’s powerful support in Congress. “They’re only concerned about selling more guns,” he said. “We have to reject and call out the politicians who support that dark vision for America.”
The Rev. Dr. Betty Deas Clark, the pastor of the Emanuel African Methodist Episcopal Church in Charleston, S.C., where an attacker killed nine people last year, said, “It’s a duty to speak up against the violence that we’re experiencing.”
Ms. Clark added, “It’s a call that has been placed upon us, and we must collectively answer that call.”
While Senate Democrats, including Dianne Feinstein of California and Bill Nelson of Florida, said they would begin by pushing for a vote on the measure to bar the sale of weapons to those suspected of ties to terrorist groups, Senator Richard Blumenthal of Connecticut, a Democrat, also called for an all-out ban on assault weapons.
“They are designed for the battlefield, which is where they belong,” Mr. Blumenthal said during the conference call with Mr. Schumer and reporters. “They are weapons of war, designed for mass destruction, not hunting or recreating.”
After meeting in Pittsburgh with gay and lesbian constituents, Senator Bob Casey, Democrat of Pennsylvania, also proposed banning the sale of guns to anyone convicted of a misdemeanor hate crime as defined in state, federal or tribal law.
The push for new legislation, nonetheless, seemed like it would continue to be an uphill climb. Republican lawmakers largely focused their remarks on the need to combat Islamist extremism and to prevent terrorists from reaching the United States or militarizing Americans.
“There may be an element of ‘homegrown extremism’ to the Orlando attack,” Senator John McCain, Republican of Arizona, said in a statement. “But there is little question that this massacre was inspired by the foreign terrorist ideology that ISIL espouses from its physical sanctuaries in the Middle East,” he said, using another name for the Islamic State.
Congress has refused repeatedly to take any significant legislative action to tighten gun laws after other mass shootings, including the murder of 26 people, mostly schoolchildren, in Newtown, Conn., in December 2012.
James B. Comey, the director of the F.B.I., said that Mr. Mateen had been on a watch list beginning in 2013, but that he had been removed from it in 2014 after an investigation of him was closed. The fact that Mr. Mateen had come to the attention of the authorities and was still permitted to buy high-powered weapons presented a remarkably different set of circumstances from previous attacks by lone gunmen previously unknown to the police.
Some security experts have cautioned against legislation that would block the sale of weapons to people who are on government watch lists, saying it could alert suspects that they are under scrutiny. Other experts have pushed for banning the sale of weapons to anyone on the no-fly list, since those people already know they are prohibited from air travel.
Josh Earnest, the White House press secretary, noted that President Obama has long supported banning assault weapons that would bar people from buying “weapons of war,” and said he would renew his push for a measure that would block those on “no-fly” lists because of suspected links to terrorism from purchasing a firearm.
“The responsibility right now lies with Congress,” Mr. Earnest said.