"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.