Twelve of the rifles the shooter in the Las Vegas massacre had in his hotel room were modified with bump stocks, attachments that allow semi-automatic rifles to fire at faster rates.
"In the aftermath of the evil and senseless attack in Las Vegas, the American people are looking for answers as to how future tragedies can be prevented," the statement reads.
"Despite the fact that the Obama administration approved the sale of bump fire stocks on at least two occasions, the NRA is calling on the Bureau of Alcohol, Tobacco, Firearms and Explosives (ATF) to immediately review whether these devices comply with federal law," the statement adds.
"The NRA believes that devices designed to allow semi-automatic rifles to function like fully-automatic rifles should be subject to additional regulations."
On Thursday, Kellyanne Conway, counselor to US President Donald Trump, implied that the White House is also open to discussing the banning of bump stocks.
Conway also suggested that Obama's administration is responsible for not regulating the dangerous gun accessory.
"I would just note for the viewers, that since bump stock has not been in the lexicon before, this is a device that President Obama's ATF decided would not be regulated in 2010 and I think that's an important part of this conversation," Conway said on Fox & Friends.
On Thursday, the No. 2 Republican in the US House of Representatives states that he expects Congress to implement regulations regarding the use of bump stocks.
"This is definitely an area we should look at," House Majority Leader Kevin McCarthy told the Fox News Channel.
"The one thing I do want to do is, let's let the sheriff and the authorities carry out their entire investigation. But I think this is definitely an area we're going to look [at] and be able to act on," he said, referring to the potential ban on the use of bump stock accessories.
However, some are skeptical of the NRA's support for regulation, seeing it as an effort to get around an all-out ban. Ronald Klain, an American political operative and lawyer, tweeted Thursday that the "NRA announcement is an effort to kill a congressional ban on bump stocks," adding "Don't be fooled."