Sens. Rick Scott, R-Fla., and Joni Ernst, R-Iowa, introduced a bill Thursday to reduce the risks of training foreign nationals on American military bases -- a reaction to the deadly December terrorist attack on Naval Air Station Pensacola.

The bill, called the "Secure U.S. Bases Act," beefs up vetting of foreign military students while also creating a more limited visa for such students and encourages the military to train members of foreign militaries overseas if possible.

"The safety and security of American men and women in uniform is always a priority for me, and it should be [a] priority of our entire government," Scott said in a statement announcing the bill's introduction. "This terrorist should never have been allowed in our country, let alone on an American military base with easy access to American military men and women."

NAS PENSACOLA SHOOTING WAS AN 'ACT OF TERRORISM', BARR SAYS; US TO EXPEL 21 SAUDI NATIONALS IN TRAINING PROGRAM

The shooting at Naval Air Station Pensacola -- in Scott's home state -- was perpetrated by a member of the Royal Saudi Air Force who was training in the United States with the American military. He killed three sailors before he was shot and killed.

It was later revealed that the killer was "motivated by jihadist ideology," according to Attorney General Bill Barr, and that he posted "anti-American, anti-Israeli and jihadist messages on social media, including two hours before the attack."

The U.S. expelled 21 Saudi nationals who were involved with the same training program. Scott has for weeks called for changes to the programs that train foreign nationals on U.S. military bases.

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"Foreign military programs have valuable benefits—providing our partners around the world the opportunity to train and learn from the best here in the U.S.," Ernst said, "but the tragic events at Pensacola underscore the unacceptable shortfalls in our security standards and vetting procedures."

Ernst on Wednesday chaired a hearing with the Senate Armed Services Committee's Emerging Threats Subcommittee on the vetting procedures used for foreign military students.

"It is critical that we learn from the attack, understand the threat, and take the necessary steps to ensure the protection of our servicemen and women going forward," she said in the hearing.

Fox News' Travis Fedschun contributed to this report.