House leaders on Thursday unveiled bipartisan legislation to tighten rules on visa-free travel by millions of foreigners to the United States in hopes of making the U.S. less vulnerable after the Paris attacks.

Republicans are promising a vote next week, and Democrats have signed on as well. The proposal may end up being added to the massive spending measure that's the main piece of remaining business in Congress this year.

The bill would require U.S. visitors from the 38 "visa waiver" countries, including the United Kingdom, France, and Spain, to go through stricter screening procedures and obtain visas if they've recently been in Iraq, Iran, Syria or Sudan. Participating countries would be required to share counterterrorism information with the U.S., and would be terminated from the program if they fail to do so.

The legislation would also mandate new fraud-resistant passports with chips containing biometric information such as fingerprints. Countries participating in the program would have to more thoroughly screen travelers, including checking them against INTERPOL databases, to be more certain that they don't have terrorist ties.

"For terrorists, travel documents are as important as weapons. That was certainly the case on 9/11, and unfortunately, it holds true today," said top bill sponsor, Rep. Candice Miller, R-Mich. "It is imperative that we address every vulnerability that might allow terrorists to carry out another attack on U.S. soil — including vulnerabilities with our visa waiver program."

The measure comes on the heels of a more partisan proposal that passed the House last month that would make it more difficult for Syrian and Iraqi refugees to enter the U.S. That measure passed by a veto-proof margin despite opposition from President Barack Obama. But the Senate has shown more interest in the visa waiver issue and Senate GOP leaders have yet to press the refugee issue.

The legislation was initially approved by the House Homeland Security Committee in June but gained momentum after the attacks in Paris — conducted chiefly by French and Belgian nationals who could easily have travelled to the U.S.

The large scope of the visa waiver program — it admits some 20 million visitors to the U.S. each year — makes it a potential security concern.

By contrast, the number of Syrian refugees entering the U.S. is much smaller, numbering fewer than 2,500.