Alshamrani, a 21-year-old second lieutenant in the Saudi Royal Air Force, opened fire in a classroom at the base on Friday, killing the three sailors and wounding eight other people before being shot dead by police.
The FBI said Sunday the shooting was being investigated with the “presumption” it was an act of terrorism, but that authorities had yet to make a final determination.
Alshamrani was reported to have posted a manifesto on Twitter before the shooting denouncing America as “a nation of evil.”
“We need to suspend the program until we investigate,” Senator Lindsey Graham, an influential Republican on national security issues, said on Fox News.
“I like allies. Saudi Arabia’s an ally, but there’s something really bad here fundamentally. We need to slow this program down and reevaluate,” he said.
US media reported that six Saudi nationals also assigned to the base have been questioned, and that Alshamrani had shown videos of mass shootings at a dinner party the night before the attack.
In a pre-taped interview that aired on Fox News Sunday, Esper confirmed that several Saudis have been detained, including “one or two” who filmed the shooting on their cellphones.
He said it was unclear if they began filming before the shooting began or after it started.
The attack has struck a live nerve in the United States with its echoes of the September 11, 2001 attacks, in which Saudi citizens accounted for 15 of the 19 hijackers that flew airliners into the World Trade Center and the Pentagon.
Saudi Arabia remains one of the closest US allies in the Middle East, and US President Donald Trump has cultivated its controversial de facto ruler, Crown Prince Mohammed bin Salman.
But Representative Matt Gaetz, a Republican whose Florida district includes the Pensacola base, warned the shooting “has to inform on our ongoing relationship with Saudi Arabia.”
Speaking on ABC’s “This Week,” he called for the military training program to be halted “until we are absolutely confident in our vetting program.”
He said he told the Saudi ambassador “as clearly as I possibly could that we want no interference from the kingdom as it relates to Saudis that we have.
“And if there are Saudis that we do not have that may have been involved in any way in the planning, inspiration, financing or execution of this, that we expect Saudi intelligence to work with our government to find the people accountable and hold them responsible.”
“And I was given every assurance from the ambassador that that would occur,” he said.
Democrats questioned the broader security relationship under the Saudi crown prince, citing Riyadh’s role in the brutal war in Yemen and the 2018 assassination of Saudi dissident Jamal Khashoggi, a columnist for The Washington Post.
Saudi Arabia has yet to account for Khashoggi’s murder at its Istanbul embassy, said Representative Zoe Loghren. “So yes, there are a lot of questions about Saudi Arabia,” she said on ABC.
“This is a relationship that has serious problems,” said Cory Booker, a senator and presidential candidate.
“And the fact that this president seems, in a very transactional way, doubling down on the relationship, and telling us it’s because of just financial interests, is unacceptable.”
Adam Schiff, the chair of the House Intelligence Committee, said it was too early to say the shooting was an act of terrorism but that Congress would press for a full investigation by the Saudis.
“And I wish the president of the United States, rather than trying to speak for the Saudi government, were pressing the Saudi government for answers,” he added on CBS’s “Face the Nation.”
Saudi Arabia’s King Salman has denounced the shooting as a “heinous crime” and said the gunman “does not represent the Saudi people.”
Prince Khalid bin Salman, the king’s younger son and the deputy defense minister, offered his “sincerest condolences” to the victims’ families.
“I was trained in a US military base, and we used that valuable training to fight side by side with our American allies against terrorism and other threats,” Prince Khalid added on Twitter.
Trump said King Salman and the crown prince would “help out the families very greatly,” without specifying how.