The "Arab Project in Iraq" lobby group "sees their opportunity to ask for compensation from the United States over violations by the US forces following the US invasion that saw the toppling of late President Saddam Hussein in 2003," the Al-Arabiya news channel reported on Saturday.
"It urged for a full-fledged investigation over the killing of civilians targets, loss of properties and individuals who suffered torture and other mistreatment on the hand of US forces."
The Iraqi group is the first to take advantage of the precedent set by JASTA in overturning the principle of sovereign immunity.
President Obama had attempted to veto the legislation, but his veto was overturned by the Senate on Wednesday. By passing JASTA and allowing 9/11 families to sue Saudi Arabia, the Senate has also made the US vulnerable to legal action seeking compensation for its foreign policy activities across the world.
The day after the Senate vote, former Republican Senator Larry Pressler expressed fear that as a veteran of the Vietnam War, he could now face legal action.
"As a Vietnam combat veteran, I could almost certainly be sued by the Vietnamese government or by a Vietnamese citizen," Pressler wrote in The Hill.
"The Gulf War, Iraq War and Afghanistan War veterans are more protected by constitutional congressional actions, but we Vietnam veterans will be raw targets if Americans can sue Saudi Arabia."
Saudi Arabia denies any culpability for the 9/11 attacks, and has warned that it might be forced to sell off billions of US assets to avoid sanctions if JASTA became law, a move which would destabilize the US dollar.
"Saudi Arabia would be forced to sell up to $750 billion in Treasury securities and other assets in the United States before they could be in danger of being frozen by American courts," Saudi Foreign Minister Adel al-Jubeir told the US Congress in March, the New York Times reported.