As the debate over strengthening gun laws becomes increasingly tense on Capitol Hill, an overwhelming number of Americans are backing one key firearm proposal: Keeping guns from people on a terror watch list.

A new Quinnipiac University poll released Thursday found that 86 percent of registered voters back such "no fly, no buy" gun legislation, compared with 12 percent that don't. And of those voters in households with a gun, 83 percent still back the proposal, versus 14 percent that don't.

A majority of voters also believe "it's possible to make new gun laws without interfering" with Americans' gun rights, 64 to 28 percent. Of those with firearms in their households, the number supporting drops to 59 percent, versus 33 percent that don't believe that.

More than nine in 10 Americans (93 percent) also think that background checks should be required for all gun buyers. Just six percent do not believe that. In households with guns, 92 percent of voters believe universal background checks should be instituted, compared to eight percent that don't. On a wholesale ban on assault weapons, 59 percent of Americans support it, compared to 37 percent that don't.

Get Breaking News Delivered to Your Inbox

The poll also found that about 38 percent of Americans have a favorable view of the National Rifle Association, the United States' most prominent pro-gun lobby, compared to 36 percent that have an unfavorable opinion of the group.

Quinnipiac also asked voters whether they supported Donald Trump's proposed Muslim ban, which the presumptive GOP nominee has seemed to soften on in recent weeks. Fifty-two percent of respondents said they opposed temporarily banning Muslims from the U.S. who aren't citizens, compared to 40 percent that backed the proposal.

Quinnipiac University surveyed 1,610 registered voters nationwide from June 21-27. The poll had a margin of error of 2.4 percentage points.