Thorbjoern Jagland, the head of the Council of Europe, the continent's top human rights agency, praised the crackdown, but said care must be taken to ensure fair trials.
"I would like to commend the Greek government for having taken action immediately, and very strong action. I think it's very important to differentiate between political work and criminal acts," Jagland told The Associated Press in an interview at the start of a two-day visit to Athens to discuss combating extremism and hate speech.
Golden Dawn says the prosecution of its members is politically motivated.
The fatal stabbing last month led to increasing calls for the party to be banned outright. But Jagland cautioned that could backfire, with similar cases elsewhere in Europe leading to parties re-emerging under different names, or going underground where they are harder to monitor and regulate.
"What is very important is to go after people that are doing crimes, and not mixing up that with politics," said Jagland, who also heads the committee which awards the Nobel Peace Prize.
He didn't comment directly on the party funding bill, saying this was "up to the Greek government," but noted that such a move would not contravene European human rights laws.
"It is actually in most European countries unlawful to do hate speech, incitement to violence, open racism and also denial of the Holocaust," he said.
During a meeting with Public Order Minister Nikos Dendias, the Council of Europe head also offered the support of the organization's legal experts in seeking ways to deal with the Golden Dawn issue.
Jagland was also to meet Wednesday with Greece's prime minister and the ministers for justice and foreign affairs.
Formerly a fringe party, Golden Dawn's popularity soared in recent years as the country sank into a financial depression and unemployment spiraled. Running on an anti-immigrant campaign, it won 18 seats in Parliament and nearly 7 percent of the vote in 2012 elections.
Party members and supporters have long been blamed for violent attacks, mostly against dark-skinned immigrants but also against left-wing political opponents and gays. Golden Dawn denies any involvement.
"This legal amendment belongs in the trash it's illegal and unconstitutional," Golden Dawn spokesman and parliament member Ilias Kasidiaris said before the vote.
"They have made this attack on us based on false testimony ... We are the only political party that doesn't play ball with the corrupt system. That is why they are after us."
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Associated Press writer Nicholas Paphitis and Derek Gatopoulos contributed.
