Republican lawmakers from Florida who are strong allies of President Trump are pressing the administration to respond more aggressively after a Saudi Air Force officer gunned down three U.S. sailors on Friday at a naval base in Pensacola, Florida.

Driving the news: Florida Sen. Rick Scott told Fox News "we need to suspend this program" of training foreign nationals on military bases while the administration reviews the circumstances that allowed the Saudi Air Force officer to murder U.S. sailors at the naval base in Pensacola.

President Trump and Defense Secretary Mark Esper both said they would review the foreign nationals' training program in light of the attack.

Republican Rep. Matt Gaetz, whose congressional district includes the Pensacola base, said on ABC's "This Week" that the Saudi attack was an "act of terrorism" and that the shooting should "inform our ongoing relationship with Saudi Arabia."

Both Gaetz and Scott have urged the Saudis to fully cooperate with the investigation and not to interfere in any way with U.S. law enforcement's questioning of Saudis who may have knowledge of the attack.

Behind the scenes: Trump immediately struck a conciliatory tone toward King Salman of Saudi Arabia. A senior administration official said the president's initial tweet, after his phone call with King Salman, was ill-advised given it came before law enforcement had established the facts about the shooter's motives or whether other Saudis were involved in planning the attack.

"King Salman of Saudi Arabia just called to express his sincere condolences and give his sympathies to the families and friends of the warriors who were killed and wounded in the attack that took place in Pensacola, Florida," Trump tweeted on Friday.

"The King said that the Saudi people are greatly angered by the barbaric actions of the shooter, and that this person in no way shape or form represents the feelings of the Saudi people who love the American people."

The official said more skepticism was warranted — even though Saudi Arabia is an important Middle East ally who helps counter Iran — given America's complicated recent history with the kingdom.

15 of the 19 al-Qaeda terrorists who staged the 9/11 attacks were Saudis. And some members of Congress have been pressing the Trump administration to reevaluate its relationship with Saudi Arabia in light of the kingdom's bombing of civilians in Yemen and murder of Washington Post columnist Jamal Khashoggi.

Go deeper: What we know so far about the Pensacola attack