Golden Dawn members of Parliament said two unidentified assailants wearing helmets drove up to the party's offices in Neo Iraklio on a motorbike and opened fire with a rifle from close range before riding off, the Athens-Macedonian News Agency reported.
The wounded man was hospitalized in serious condition, the news agency said.
Golden Dawn said in a release that there were a number of people standing about when the attack occurred. The party officials' statement said the two men killed were ages 22 and 26.
"Before driving off, the terrorists shot again against the victims lying dead on the ground," party officials said. "They literally emptied their guns on them. Another citizen was seriously injured by a bullet. It is a miracle that there were no more victims. The blow was blind and the culprits were determined to kill anyone who was at the Golden Dawn offices at the time."
Police recovered a motorcycle nearby that they believed had been stolen and used in the attack.
The New York Times reported an unidentified police spokesman said it was premature to say whether the 7 p.m. attack was political.
Public Order Minister Nikos Dendias said authorities "will not allow the country to become an arena for scores to be settled, for whatever reason," the newspaper said.