Just how many troops were killed or wounded by Iranian-supplied weaponry during the Iraq war remains in dispute. The United States military said in 2015 that during a six-year stretch, E.F.P. attacks killed 196 American troops and wounded 861 others. More recently, the Pentagon has given an estimate of 600 American troop deaths from roadside bombs and various other attacks supported by Iran during the war.

Some experts, like Joe Cirincione, who was a longtime Democratic staff member in Congress, said evidence had never been presented to blame General Suleimani for 600 deaths or the “thousands” of casualties that Mr. Trump is now citing. But he said there was no question that Iran bears considerable responsibility.

“Can you pin every single E.F.P. attack on Suleimani? No, that’s going too far,” said Mr. Cirincione, who is now the president of Ploughshares Fund, a global security foundation. But, he said, “I’ve never heard anyone claim the Iranians did not supply these weapons.”

General Suleimani once sought to plead his innocence. In January 2007, the general told Jalal Talabani, the Iraqi president at the time, that his hands were clean, according to an American diplomatic cable later revealed by WikiLeaks.

“I swear on the grave of Khomeini I haven’t authorized a bullet against the U.S.,” the general said.

Patrick Farr, another plaintiff in the suit, does not believe him.

Mr. Farr’s son, Clay, a soldier on his first deployment in Iraq, was injured by a roadside bomb on the day he turned 21. The next day, he called his father from a hospital bed. It was the last time they talked. A week later, he was back in the field, and an E.F.P. struck the Humvee he was driving, killing him.