A bipartisan pair of House members has introduced a ban on the bump stock devices used to speed up the rate of fire of semi-automatic weapons –- an accessory used by the Las Vegas shooter last week.

The bill, from Reps. Seth Moulton, D-Mass., and Carlos Curbelo, R-Fla., would make it illegal to manufacture, transfer or possess "any part or combination of parts that is designed and functions to increase the rate of fire of a semiautomatic rifle."

The proposal marks a new effort to break the gun control gridlock on Capitol Hill, and has been endorsed by a group of 20 Democrats and Republicans.

Democrats, led by Reps. David Cicilline, D-Rhode Island and Dina Titus, D-Nevada have put forward their own proposal that would similarly ban bump stocks, and punish bump-stock users with ten years in prison.

The Curbelo-Moulton bill would put in place a fine or up to five years in prison for any violations. It also directs the U.S. Sentencing Commission to beef up penalties for anyone caught using a bump stock. It would also recommend additional penalties for anyone caught smuggling bump-stocks into the United States.

Titus, who represents most of Las Vegas, criticized the bipartisan bill in a statement Tuesday.

"Rep. Curbelo’s bill almost mirrors the Automatic Gunfire Prevention Act, but it carries weaker penalties for criminal violators. There is no reason to undermine our position at this point just to satisfy the NRA," Titus said in a statement.

Moulton rejected the criticism in a brief interview Tuesday.

"I don’t think that’s accurate at all," he said. "I hope she reaches out to me."

"Our bill gives very specific guidelines to the sentencing commission and suggests that they have enhanced penalties for drug crimes, for violent offenses and it also includes penalties for smuggling which is something that experts expects will happen if we are successful at outlawing bump stocks," he said. "Most important, our bill is bipartisan and I think that is the way gun reform needs to happen."

Talk of regulating and restricting bump stocks was unheard of on Capitol Hill before the deadliest shooting in U.S. history. Now, lawmakers are divided over addressing the use of bump stocks using regulation or legislation.

Some Republicans -- along with the National Rifle Association -- have called on the Bureau of Alcohol, Tobacco and Firearms to review a 2010 decision that allowed the sale of bump stocks without regulation.

A group of GOP senators led by Sen. Dean Heller, R-Nevada, sent a letter to the ATF last week asking for a review of that 2010 ruling. Rep. Adam Kinzinger, R-Illinois, is expected to send a similar letter to the ATF Tuesday.

"I think the ATF can do this quickly -- they can make a determination. If they drag their heels on it as we say in the letter, we’ll look at legislation solutions,” Kinzinger, a gun owner, told reporters last week.

House Speaker Paul Ryan, R-Wisconsin, said last week that Congress needs to “look at how we can tighten up compliance with this law.”

”Was it a regulatory misstep by ATF several years ago?” he said last week. “We all know fully automated weapons are illegal and so is this a big gap that needs to be closed? And if so, how to close it? We are all beginning to go through that analysis."

In 2010, the ATF determined that bump stocks did not meet the required criteria to merit regulation under the Gun Control Act or the National Firearms Act, because they do not technically turn semiautomatic firearms into machine guns.

David Chipman, a former ATF agent now advising the gun-control group Americans for Responsible Solutions, said it's unlikely the ATF overturns its earlier decision, given the agency's reluctance to appear political.

White House officials recently asked Justice Department officials to weigh in on whether bump stocks could be legally barred, and the consensus was that current laws and regulations made the administration unable to ban bump stocks, sources told ABC News.

Gun control advocates argue that a favorable ruling by the ATF would also be a more narrow solution than legislation, which could also cover devices similar to bump stocks.