FITZWILLIAM, N.H. -- The national debate over gun laws traveled to another New England town on Thursday, as Sen. Kelly Ayotte, R-N.H., told constituents that universal background checks could lead to a "registry" of gun owners.

"In terms of a universal background check, as it's been framed, I have a lot of concerns of that leading to a registry that will create a privacy situation for lawful firearms owners," Ayotte said.

The remarks came during a town hall here in southern New Hampshire, after a man asked, "What's wrong with universal background checks?"

The back-and-forth was another sign that Ayotte's vote against a gun bill last month continues to trail her. The bi-partisan bill, negotiated by Sens. Joe Manchin, D-W.Va., and Pat Toomey, R-Pa., would have enforced background checks for all gun buyers.

Ayotte's vote against the legislation has not only made her a target for gun control advocates nationwide, but also has left her fielding questions and complaints about her stance on the divisive topic of guns from voters across her state.

During a town hall Tuesday in Warren, N.H., Ayotte was confronted by the daughter of Dawn Hochsprung, the principal of Sandy Hook Elementary, who was killed by Adam Lanza in the Dec. 14 massacre in Newton, Conn. Later Tuesday, in Tilton, N.H., members of the audience waved signs that read, "Demand action to end gun violence."

Ayotte's comments echoed those of the National Rifle Association. Appearing on NBC's "Meet the Press" in March, NRA executive vice president and CEO Wayne LaPierre dismissed the idea of universal background checks and invoked the threat of a national gun owner's registry.

"Here's the loophole: society, the H.I.P.A.A. laws, the mental health laws, the medical records," LaPierre said. "The Adam Lanzas, the shooters in Aurora, the shooters in Newtown, they're unrecognizable. They're not going to be in the system. Who is going to be in the system? You and me. And our names are going to be in the system. There is going to be a list created; that list will be abused. Some newspaper will print it all. Somebody will hack it. There will be a registry," LaPierre continued.

Although another Newton relative was in the audience here on Thursday, he did not ask a question.

Gilles Rousseau, the father of slain teacher Lauren Rousseau, later told reporters he was there to push for background checks, but did not have an opportunity speak personally with the senator.

"I want her to reconsider a vote. This is not [a] national registry," Rousseau said.

Ayotte told the crowd that she is in favor of strengthening prosecutions of gun crime and making improvements to mental health care.