House of Representatives Speaker Paul Ryan told a radio talk show: "Clearly that's something we need to look into."
Texas Senator John Cornyn - the number two Republican in the Senate - has called for hearings into the devices.
A bump-stock attaches to the butt of a rifle, allowing the weapon to fire close to the rate of a machine gun.
Stephen Paddock, the gunman in Las Vegas, had fixed the accessories to 12 rifles.
Long fight ahead
Analysis by Anthony Zurcher, BBC North America reporter
It appears a move to ban bump-stock devices is picking up steam in Congress. Some normally staunch gun-control opponents seem willing to consider new legislation. The NRA, which opposes just about any new regulations, has gone silent.
That's going to change soon.
The challenge for gun rights supporters is a bump-stock ban opens the door for a new debate about where to draw the line over limiting a firearm's lethality. For decades it's been at how many bullets can be fired with one trigger pull.
Bump-stocks blur that line. Can you outlaw a device that helps squeeze off rounds more quickly but not think about prohibiting quick-change magazines or limiting their sizes? Or banning pistol grips, which make firing easier?
It won't take many Republicans, with the NRA looking over their shoulder, to grind the process to a halt.
Five reasons US gun control won't happen
"I didn't even know what they were until this week," Mr Ryan, a Wisconsin congressman, said on Thursday of bump-stocks.
He told talk show host Hugh Hewitt: "I think we're quickly coming up to speed with what this is."
For years Republicans in Congress, as well as conservative Democrats, have blocked gun control efforts in the wake of violent tragedies.
But now a liberal Democratic gun control measure appears to have found a receptive audience across the aisle.
Senator Cornyn said on Wednesday: "It strikes me as odd that it's illegal to convert a semi-automatic weapon to an automatic weapon, but apparently these bump-stocks are not illegal under the current law.
"I own a lot of guns. As a hunter and sportsman, I think that's our right as Americans.
"But I don't understand the use of this bump-stock."
He said his colleagues should hold hearings to discuss the legality of the devices.
How gun control fails
- In the last five years lawmakers have proposed more than 100 gun control measures - not one of them has become law, report CBS News
- Republicans blocked a measure that would have limited the bullet capacity in gun magazines after 32 were shot dead at Virginia Tech university massacre in 2007
- Efforts to expand background checks on gun sales and reinstate a Clinton-era ban on so-called assault weapons failed after 2012 Sandy Hook school shooting
- Congress rejected a bill aiming to stop suspected terrorists from legally buying guns after 14 people died in San Bernadino, California, in 2015
- Efforts to expand background checks failed again after 49 died at Pulse nightclub in Orlando, Florida, in 2016
Congressman Mark Meadows, who leads the hardline conservative Freedom Caucus, also said that he would be open to a hearing.
Since Congress passed the Firearm Owners' Protection Act in 1986, it has been relatively difficult for civilians to buy new, fully automatic weapons, which reload automatically and fire continuously as long as the trigger is pulled.
Bump-fire stocks, also called bump-stocks and slide-fire adapters, allow semi-automatic rifles to fire at a high rate, similar to a machine gun.
But the accessories can be obtained without the extensive background checks required of automatic weapons.
They typically cost less than $200 (£150) and allow nearly 100 high-velocity bullets to be fired in just seven seconds, according to one company advert.
One of the most popular manufacturers of bump-stocks, Slide Fire, said they had sold out "due to extreme high demands" since the Las Vegas shooting.
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"I think they should be banned," Republican Texas congressman Bill Flores told The Hill newspaper, adding that he had never heard of bump-stocks before.
"There's no reason for a typical gun owner to own anything that converts a semi-automatic to something that behaves like an automatic," he said.
Democratic California congressman Mike Thompson, who chairs the congressional Gun Violence Prevention Task Force, said Congress must address the "loophole".
"We don't know how many lives could have been spared in Las Vegas had the shooter not had bump-stocks," he said.