"We obtained a conviction against the American government to pay 400 million dollars for its part in the deaths on the martyrs Nasr Allah Shafiie and Nadir Mahdavi," lawyer Nassrin Niktash was quoted as telling the student news agency ISNA.
"We have asked the foreign ministry to follow this dossier to obtain payment," he said.
He said that Shafiie and Mahdavi were killed by US Marines in the 1980s, but the report did not elaborate.
According to ISNA, the court also ordered the United States to pay $800 million to two Iranians who were "kidnapped" by US forces and "suffered damage," also without elaborating.
The verdicts come following a series of cases lodged against Tehran in US courts. The Islamic republic has been ordered to pay hundreds of millions of dollars in damages following 21 such lawsuits.
In one of the most high-profile cases, a US court ruled last September that Iran had to pay more than $420 million to a dozen US victims of a 1997 bombing in Jerusalem carried out by the Palestinian resistance movement Hamas, which the court alleges is supported by Iran.
In March 2000, a US federal judge ordered Iran to pay $341 million to journalist Terry Anderson and to members of his family.
Anderson, who had been Beirut bureau chief for the Associated Press, was kidnapped by another Palestinian resistance group, Islamic Jihad, and held for more than six years.