(CNN) - Sen. Joseph Lieberman said Sunday he intends to launch a Senate committee hearing on whether the Fort Hood shootings were a terrorist act and if the Army should have taken pre-emptive steps due to reported signs of Islamic extremism by the suspected gunman.
"I'm intending to begin a congressional investigation of my Homeland Security Committee into what were the motives of (Maj. Nidal Malik) Hasan in carrying out this mass murder," the Connecticut independent, who belongs to the Democratic caucus, said on "FOX News Sunday."
If Hasan was showing signs of being an Islamic extremist, the Army should have acted on that earlier and "he should have been gone," said Lieberman, the chairman of the Senate Homeland Security and Governmental Affairs Committee.
Saying it was too early to know Hasan's exact motive, Lieberman declared that if reports of the alleged gunman's possible Islamic extremism are true, then "the murder of these 13 people was a terrorist act."
"We don't know enough to say now," Lieberman said, noting what he called "strong warning signs" that Hasan had become an Islamic extremist.
Lieberman cited reports that Hasan made statements justifying suicide bombers as similar to American soldiers that hurl their bodies on exploding grenades to protect others, and that some bystanders reported Hasan shouted "Allahu Akbar," Arabic for "God is great," which terrorists have used as a battle cry.
"If that's confirmed, it raises genuine concerns that it was a terrorist act," Lieberman said.
In addition, Lieberman noted Hasan allegedly had said he understood and supported the shooting death of a Little Rock, Arkansas, Army recruiter, allegedly by a Muslim convert.
His committee investigation would look into "whether warning signs were missed" regarding Hasan's behavior and how Hasan may have become a "self-radicalized homegrown terrorist," Lieberman said.
However, other members of Congress counseled waiting for the military and FBI to complete their investigation of what happened before reaching any conclusions.
"This man's actions reflect on him," Republican Sen. Lindsey Graham of South Carolina told the CBS program "Face the Nation." "And if we missed some signals about him that we should have known, great. But let's don't take this to a level that we should not. Let's don't accuse people of basically giving him a pass because he's a Muslim. Because I don't think there's any evidence of that."
U.S. Army Chief of Staff Gen. George Casey told CNN that an investigation of the shootings by the Army and FBI would help answer such questions.
"There's been a lot of speculation going on, and probably the curiosity is a good thing," Casey told the CNN program "State of the Union." "But we have to be careful, because we can't jump to conclusions now based on little snippets of information that come out."
Casey said he was "concerned that this increased speculation could cause a backlash" against Muslim soldiers.
"I've asked our Army leaders to be on the lookout for that," Casey said. "It would be a shame - as great a tragedy as this was - it would be a shame if our diversity became a casualty as well."