"We will not let democracy succumb to criminal violence under any circumstances," Samaras told Mega television channel in an interview. "We will be relentless against those responsible."
On Friday, two armed assailants riding a motorbike shot dead two members of Golden Dawn and seriously injured a third one in a shock drive-by attack outside the party's offices in an Athens suburb.
Experts fear the attack could spark further violence, as it followed the September assassination of an anti-fascist rapper by a Golden Dawn member.
Police today released security camera footage of one of the alleged attackers, saying they were looking for a thin man up to five feet seven inches tall, wearing jeans, white shoes and carrying a backpack.
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Samaras warned that Greeks had to stand united to address the economic crisis still gripping the nation, three years after it narrowly avoided bankruptcy with the aid of EU-IMF loans.
The premier said the double murder was "like lighting a match in a powder magazine, at a moment when we have so many other fires, economic (fires) before us".