The mayor of Dayton, Ohio, urged Congress on Wednesday to pass a ban on military-style “assault” weapons, saying that getting those weapons off the streets could have affected the mass shooting in her city last month.

“I’m here to ask you to do something,” Nan Whaley told the House Judiciary Committee, which was examining the merits of a gun ban.

But the panel also heard from gun rights advocates who warned lawmakers against passing such a far-reaching proposal and “legislating” law-abiding Americans into “being criminals.”

The hearing made good on House Democrats’ vow to put the gun issue at the top of their priority list in the current Congress. Gun control gained renewed attention in the wake of the shootings last month in Dayton and El Paso, Texas, where more than 30 people were killed in the two cities.

Ms. Whaley said a proposal from Rep. David Cicilline, Rhode Island Democrat, to ban certain military-style weapons is “very thoughtful” and “should move forward.”

“That bill would affect the Dayton shooting, frankly, and so it would make a great difference so there won’t be cities like Dayton that have experienced this kind of trauma,” she said.

A gunman armed with AR-15-style pistol shot and killed nine people and wounded dozens of others at a popular nightclub area of Dayton last month.

Ms. Whaley also said the police officers who were nearby and ran toward the shooting “saved countless lives.”

“And if we did not have, as I like to say, six good guys with guns, the amount of damage and death that would have happened could have been in the hundreds,” she said.

In the wake of the two shootings, though, some say that simply banning the manufacture and sale of military-style, semiautomatic firearms isn’t enough and that the federal government should institute an Australian-style buyback scheme.

“If these weapons are dangerous in the future, wouldn’t you agree that they’re dangerous now and that there has to be some way to protect people now from ever having their kids shot in school, their parent shot in a church, their sister shot at a concert, from one of these weapons?” said Rep. Eric Swalwell, California Democrat and a former 2020 presidential candidate.

Former Rep. Beto O’Rourke has aggressively pushed a mandatory buyback scheme on the presidential campaign trail and vowed in the last debate to “take” popular semiautomatic rifles, such as the AR-15, away from owners.

But David Chipman, a former federal agent who is now a senior adviser to former Rep. Gabrielle Giffords’ gun control group, suggested to lawmakers Wednesday that using the existing National Firearms Act to impose new regulations on the weapons would be a better route.

“I think that we should be looking to America, not Australia, for solutions,” Mr. Chipman said. “The NFA was passed at a time where we had a similar problem so I would suggest that it’s a balance that would honor the rights of people who have these guns to keep them if they were properly regulated.”

Several witnesses, though, said banning the weapons wouldn’t necessarily do much to reduce the likelihood of mass shootings and that the new regulations could turn otherwise law-abiding Americans into criminals overnight.

“We are law-abiding, responsible gun owners and please don’t legislate the 150 million people just like me into being criminals,” said Dianna Muller, founder of the D.C. Project.

She pointed to the Trump administration’s recent ban on bump stock devices that allow semiautomatic weapons to mimic the rate of machine gunfire as a recent example.

“I was a bump stock owner, and I had to make a decision: do I become a felon or do I comply?” she said. “I will not comply with the assault weapons ban.”

Congress had passed an assault weapons ban in 1994, but it lapsed in 2004.

Despite the renewed attention on the gun issue, a new ban on such weapons is on the outer edge of what could reasonably be expected to pass Congress in the near future.

Congressional Democrats have instead urged Senate Majority Leader Mitch McConnell to take up House-passed legislation that would expand federal background checks to cover more gun sales and extend the time dealers have to wait to hear back from the FBI before proceeding with a sale.

But Mr. McConnell has said he’s waiting for more specifics on what President Trump would support.

Mr. Trump said he talked about guns with House Speaker Nancy Pelosi on Tuesday, but that Mrs. Pelosi isn’t interested in pursuing the issue as House Democrats formalize their impeachment investigation.

“Nancy Pelosi is not interested in guns, in gun protection, in gun safety,” Mr. Trump said Wednesday while in New York at a United Nations meeting. “She’s been taken over by the radical left.”

But Mrs. Pelosi, who joined gun control advocates at a rally near the Capitol on Wednesday, had expressed hope that she could continue to work with the president on legislation.

“That’s not what he told me,” she said about the notion that the impeachment inquiry destroyed any chance at legislation, according to Reuters.

Attorney General William Barr recently floated a proposal to expand background checks to cover more commercial sales, along the lines of what GOP Sen. Pat Toomey of Pennsylvania and Democratic Sen. Joe Manchin III of West Virginia proposed several years ago.

But conservatives objected and the White House quickly disowned the document.

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