Cornyn has asked Judiciary Committee Chairman Charles Grassley, R-Iowa, to convene a hearing to explore the issue of banning bump stocks - and possibly other issues that arise from the Las Vegas investigation.
Other proposals introduced in Congress this year have included allowing concealed-carry permits to apply across state lines and a bill that was expected to come up in short order until the mass shooting in Las Vegas that would make it easier for more people to buy suppressors, which limit the sound and light emitted from a fired weapon.
"We certainly welcome that, would like to be part of that conversation", Sanders said on Thursday.
For his part, Ryan has said he'd be open to a vote on banning the bump stock devices. They can fit over the rear shoulder-stock assembly on a semi-automatic rifle and with applied pressure cause the weapon to fire continuously, increasing the rate from between 45 and 60 rounds per minute to between 400 and 800 rounds per minute, according to Feinstein's office.
The National Rifle Association has said the device used to modify the Las Vegas gunman's weapons should be subject to more regulation. Dianne Feinstein, a Democrat and longtime proponent of gun control, introduced the measure Wednesday.
"Automatic weapons are illegal", Wisconsin Sen.
Echoing a sentiment circulating around conservative media, White House counselor Kellyanne Conway pointed out on "Fox & Friends" on Thursday that in 2010, the Bureau of Alcohol, Tobacco, and Firearms decided against classifying the weapons as automatic.
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While the White House has said it was too soon to talk about gun regulations, press secretary Sarah Huckabee Sanders said they welcomed the talk about gun modifiers. "So I really see that for the first time we may have a chance at getting a bipartisan solution to this great challenge".
Many Republicans echoed Ryan, saying the entire concept of bump stocks was new to them and holding off from a commitment to the call for a legislative ban. "The best part is we all know there are people who watched this, shared it and commented on the video who fully believe what he did would actually work".
West Virginia residents "cherish the right to be able to go hunting with their family. sport shooting and all the things we do enjoy", Manchin said, adding that any potential legislation must be based on common sense. The legality of bump stocks could hinge on a "technicality", he said.
The most prominent USA gun lobby group on Thursday said it agrees to placing restriction on a device that accelerates gunfire, after a version of it was discovered in the arsenal of Las Vegas killer Stephen Paddock, who was behind the deadliest mass shooting in modern US history.
The association bans the use of these devices in some of their own firing ranges, Politico reports.