Investigators are examining "all avenues, particularly those that link these events to extremist groups" behind a series of attacks on politicians, police, banks and the media, according to one source.
Attacks by groups describing themselves as revolutionary and anti-authoritarian are relatively common in Greece.
They are not usually fatal, although in 2009 a police officer was killed by three unknown gunmen in Athens and in 2010 a journalist was shot dead at his home. Both killings were claimed by the Sect of Revolutionaries, an extremist group.
The Sect of Revolutionaries has been quiet of late, but another extremist group called the Conspiracy of Fire Nuclei has claimed responsibility for a series of recent attacks including a bomb attack on the car of the Athens prison director.
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The two men killed on yesterday were aged 22 and 25. Their identities have not been made public but a spokesman for Golden Dawn said they were members.
The party had planned a meeting yesterday night in the Athens suburb of Neo Iraklio, where the shooting took place.
The attack happened about a month and a half after the killing of an anti-fascist musician by a self-confessed neo-Nazi.
The September 18 murder of hip hop artist Pavlos Fyssas by a Golden Dawn supporter had triggered public outrage, putting pressure on Greek authorities, who launched a crackdown on the party.
Greece's public order minister Nikos Dendias yesterday expressed his "sadness at the death of the young men".
Golden Dawn is Greece's third-most-popular party, with 18 seats in parliament.