Former Secretary of State Hillary Clinton delivered an apparent rebuke to conservative gun advocates during an appearance on CNN on Tuesday, saying she would support a ban on assault weapons.

“We cannot let a minority of people — and that’s what it is, a minority of people — hold a viewpoint that terrorizes the majority of people,” Clinton said in response to a question during a town hall forum. “You are about the fifth person in the past few weeks — parents, another teacher, interested citizens — who have said something similar to me.”

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Clinton, the presumptive front-runner for the Democratic Party presidential nomination if she enters the 2016 campaign, also alluded to widespread national support for more comprehensive gun legislation shortly following the December 2012 mass shooting at Sandy Hook Elementary in Connecticut.

“Yes, we need to thrash this out in the political realm,” she said. “But the vast majority of Americans, even law-abiding gun owners, want background checks that work. Information that is shared immediately, and an awareness that we’re going to have to do a better job protecting the vast majority of our citizens, including our children, from that very very very small group.”

Watch Clinton’s remarks, as aired by CNN on Tuesday, below.