Murphy said he would introduce a new background check bill and House Democratic leader Nancy Pelosi also urged passage of legislation toughening checks on gun sales.
White House spokeswoman Sarah Sanders, asked whether President Donald Trump might now favor tighter gun laws, told reporters: "I think that's something that we can talk about in the coming days and see what that looks like moving forward".
Rep. Chris Collins, R-N.Y., said action on guns after Las Vegas was unnecessary. "We'd like to be a part of that conversation".
"The National Rifle Association is calling on the Bureau of Alcohol, Tobacco, Firearms and Explosives (BATFE) to immediately review whether these devices comply with federal law", the NRA said in a statement. And the group's decision to be for further regulation of bump stocks is clearly a strategic move aimed at avoiding any more sweeping or comprehensive attempts at gun control. Gun company stocks rose in market trading following Sunday's attack. "We booked this a long time ago", one said.
Mr Trump had reportedly discussed the issue with lawmakers on the way back from visiting Las Vegas on Wednesday. That disgusting sound also alerted hundreds of people at the music festival in Las Vegas to try to take cover.
A USA law enforcement official, speaking on condition of anonymity, told Reuters authorities believe 64-year-old Stephen Paddock had at least two such weapons when he fired from his 32nd-floor hotel room, killing at least 59 people and injuring more than 500.
In a probable effort to avoid controversy, Wal-Mart Stores Inc and sporting goods store Cabela's both appeared to pull bump stocks from their websites on Wednesday. They are two of many thousands whose lives have been needlessly lost to gun violence.
Gun Owners of America executive director Erich Pratt defended the use of bump stocks, stating that gun advocates use them for entertainment.
It was a rare concession for all concerned. The nation's largest gun lobby and most Republicans have stood firmly in recent years against stricter gun regulations, even as one mass shooting after another horrified the nation.
Several leading Congressional Republicans have indicated this week that they are open to considering additional regulations on bump stocks, or even banning them altogether. There are reasonable and realistic steps we can take to make it harder for people to commit suicide with a gun, or perpetrate domestic violence, or go on one of the terrifying mass shootings that have become all too common.
Robert Spitzer, chairman of the political science department at SUNY Cortland, who watches the gun industry closely, said he was surprised. But to do that, the left must first stop making stuff up about guns. Will we wait until the development of a nuclear pistol before we realize that we must control all weapons in this country? "It's a very specific accessory".
The bump stock causes the gun's recoil to press against the shooter's finger after each shot, firing rounds much more quickly than possible by pulling it manually. It includes a grip that keeps the trigger finger at a static position.