Two members of Greece's Golden Dawn shot dead
The attack comes weeks after several members of Golden Dawn, including the leader, were arrested on suspicion of forming a criminal organisation.
The arrests followed the killing of an anti-fascist musician.
A Golden Dawn supporter has been charged over the killing of Pavlos Fyssas, 34, whose stage name was Killah P.
His death sparked protests in Athens and across Greece.
Government vow The two men who died on Friday were shot at close range from a motorcycle carrying two men, said Golden Dawn MP Georgios Germenis.
"A man got off a motorcycle wearing a helmet and shot them,'' he said.
A third man was seriously wounded, and taken to hospital, said police.
Following the shooting, in the Neo Iraklio suburb of Athens, anti-terrorist police wearing riot gear cordoned off the area around the offices.
The BBC's Mark Lowen in Athens says 15 bullets were said to have been found at the scene, from 9mm handguns, and police are surveying CCTV footage from cameras at the party office.
He says the fear now is that an atmosphere of revenge could develop.
"The murderers - whoever they are - will be dealt with unsparingly by our democracy. Let everyone know this," a government spokesman, Simos Kedikoglou, told reporters.
The shooting comes after the Greek government launched a crackdown on Golden Dawn, including raids on the party's offices, followed the killing of Pavlos Fyssas on 17 September.
George Roupakias, 45, who said he was a supporter of Golden Dawn, was later charged with voluntary manslaughter and illegal possession of a weapon.
Meanwhile, the leader of Golden Dawn, Nikolaos Michaloliakos, and two other senior party MPs are currently in jail, awaiting trial on charges of forming a criminal group. They deny the charges.
Last week the Greek parliament voted to suspend state funding for Golden Dawn, which is the third most popular party in Greece.
The new law allows an indefinite freeze on funding for parties whose leadership is charged with involvement in terrorism, or a criminal group.