WASHINGTON (Reuters) - Two Republicans and two Democrats took a first bipartisan step toward new gun restrictions on Tuesday by introducing a bill in the House of Representatives to crack down on gun trafficking to criminals.

The bill, strongly backed by law enforcement groups, would strengthen penalties on "straw purchasers," who buy guns for those who are barred by law from buying their own weapons.

The sponsors said the measure would help stop the flow of guns to criminals without infringing on the constitutional rights of lawful gun owners.

"For too long, we have been handcuffing the wrong people. We have made it too hard for law enforcement to stop guns from getting into the hands of criminals and too easy for criminals to get their hands on guns," said U.S. Representative Carolyn Maloney, a New York Democrat and one of the four co-sponsors.

The other sponsors are Republicans Patrick Meehan of Pennsylvania and Scott Rigell of Virginia, and Democrat Elijah Cummings of Maryland.

The bill is the latest of several proposals in Congress to curb gun violence since a gunman shot dead 20 children and six adults on December 14 at an elementary school in Newtown, Connecticut, in a massacre that sparked public outrage.

President Barack Obama and other Democrats have offered a broad package of gun-control restrictions, including proposals similar to the gun-trafficking measure, but many will face steep hurdles to approval in Congress, particularly in the conservative Republican-led House.

Sponsors of the gun trafficking bill said its bipartisan support and heavy backing by law enforcement groups could make it attractive to both sides in the growing gun debate.

"We have a message for our colleagues in the House," Cummings said. "This bill simply makes sense. Law enforcement officials have asked for it. It will make a significant difference in combating gun crime. And it will not affect the rights of a single legitimate gun owner."

Representatives of law enforcement groups appeared at a news conference to unveil the bill, which makes it a federal crime to purchase or transfer a gun if the intent is to deliver it to someone prohibited by law from owning one.

The measure would strengthen penalties to up to 20 years in prison for "straw purchasers" who intentionally provide false information when they buy guns. It also would increase penalties for organizers of drug trafficking networks, the sponsors said.

The Senate Judiciary Committee plans to unveil the gun-control bills from Obama by the end of the month, and House Republican leaders have said they want the Senate to go first on the issue.

Obama's proposal to expand background checks on gun sales is considered the most likely item to pass Congress. The No. 2 House Republican, Eric Cantor of Virginia, told CNN on Tuesday he would support improvements in background checks for gun sales that ensured mental health information was linked to the databases used.

(Reporting by John Whitesides; Editing by David Brunnstrom)