American lawmakers voted overwhelmingly Tuesday to impose restrictions making it more difficult for visitors to Iraq, Syria and countries listed as supporting terrorism to travel visa-free to the United States.

The House of Representatives voted 407 to 19 in support of the Visa Waiver Program Improvement Act of 2015, a bill backed by the White House in the aftermath of the deadly attacks in Paris that were conducted by extremists who could have traveled to America without a visa.

It would bar people who traveled after March 1, 2011 to Iraq and Syria, as well as Iran and Sudan, from participating in the visa-free program, require the use of electronic passports for all participating countries, and call for participating countries to share more intelligence data on suspected terrorists and criminals.