Greek Prime Minister Antonis Samaras has said he will not let neo-Nazi party Golden Dawn “undermine” democracy.
His remarks came after a Golden Dawn supporter allegedly admitted killing an anti-fascist activist.
“This government is determined not to let the descendants of the Nazis poison our social life or commit crimes,” Mr Samaras said in a national TV address.
Hundreds of mourners attended the funeral of Pavlos Fyssas, 34 – stabbed to death on Wednesday near Athens.
There is profound anger in Greece over the events, the BBC’s Mark Lowen in Athens reports.
The far-right party Golden Dawn has been blamed for a tide of attacks on immigrants.
Greece’s deputy PM said it must now be treated as a “criminal organisation”.
In a graveyard in Athens cemetery, more than 2,000 mourners bid farewell to Mr Fyssas, an anti-racism rapper who went by the stage name Killah P.
“Pigs! Fascists! Murderers!” mourners chanted, the Reuters news agency reports.
Mr Fyssas’s white coffin was carried by his relatives onto a hill near the suburb of Keratsini were he was stabbed.
As others sang his songs, one man shouted: “Immortal!”
Several rallies by anti-establishment groups and unions, which turned a 48-hour anti-austerity strike into a protest over his killing, were planned for later on Thursday.
The 45-year-old suspected killer, who has been pictured in Greek media with his arm around a Golden Dawn lawmaker, was due to appear before a prosecutor on Saturday.
Golden Dawn, Greece’s third most popular party, condemned the killing and denied involvement in the attack. It said those who accused the party were “wretched sycophants” trying to win votes.
But Evangelos Venizelos, who is the head of the Pasok socialist party, the junior party in the coalition government, said Golden Dawn had “violence as its priority”.
He and Prime Minister Samaras have agreed to use all available legal powers to crack down on the movement, Greek daily Kathimerini reports.
The BBC’s Mark Lowen reports on the clashes in Athens
Thousands of people rallied on Wednesday at the spot where Mr Fyssas was killed.
Violence broke out in the evening, when youths set fire to rubbish bins, broke up paving stones and threw pieces at police, who fired volleys of tear gas. At least 23 people were arrested.
There were also clashes at demonstrations in the cities of Thessaloniki and Patras.
Golden Dawn denies being a neo-Nazi movement, though its badge resembles a swastika, some senior members have praised Adolf Hitler, and its members wear black T-shirts and combat trousers at anti-immigrant demonstrations.
It came from nowhere to win nearly 7% of the vote in 2012 general elections and took its place in parliament. Opinion polls suggest its support has risen still higher.
A number of reports, including some gathered by the BBC, have suggested there are strong ties between Golden Dawn and elements of the Greek police.