The violence began after dozens of hooded demonstrators, some wearing motorcycle helmets, broke off from the initially peaceful march that police blocked from reaching the party`s offices. Police chased small groups of protesters through the streets.
Golden Dawn is Greece`s third most popular party and the most visible symptom of discontent over state corruption and a deep economic crisis that has fuelled hostility to immigrants.
But polls since the killing of rapper Pavlos Fissas indicate the party has lost about a third of its public support.
Wednesday`s rallies by university students, labor unions and leftists in Athens and the second biggest city Thessaloniki have overshadowed a 48-hour public sector strike over layoffs demanded by Greece`s international lenders.
More than 10,000 people, some holding banners reading "Never Again Fascism" and singing anti-fascism anthems, marched outside parliament in the central Syntagma Square, where hip-hop groups held a memorial concert earlier on Wednesday.
The protest column then headed for Golden Dawn`s headquarters 5 km (three miles) from central Athens.
The killing of 34-year-old Fissas has fired outrage across the political spectrum against a party that is widely regarded as neo-Nazi and whose popularity has so far appeared immune to accusations of brutality and violence.
Golden Dawn rejects the neo-Nazi label and any involvement in the attack, saying it is the target of a witch-hunt after the government began efforts to crack down on it and its alleged influence over the Greek police force.
"NO TO FASCISM"
"The crisis brought us to our knees but we need to say a loud `no` to fascism like we did in `74," said Vangelis Georgountzos, 59, referring to the student uprising that led to the overthrow of Greece`s then-ruling military junta.
Standing in the crowd that flooded the street in front of parliament alongside his teenage daughter, Georgountzos said: "First it was the immigrants, then Fissas, tomorrow it could be your son or daughter - everyone needs to understand this."
Earlier in the day, mourners laid flowers and candles at the spot in the working-class neighborhood of Keratsini where Fissas, who performed anti-racism raps under the stage name Killah P, was knifed.
"Murderers!" declared a banner above the makeshift shrine.
An ALCO survey for the Newsit.gr website, conducted in the days after the stabbing, found that public support for Golden Dawn was down by 4 percentage points to 6.8 percent.
"Golden Dawn voters haven`t changed their minds, they`re simply not saying who they`ll vote for because of the current climate of terror," the party responded in a statement.
The party says petrol bombers have attacked its offices in recent days and that assailants smashed the window of an animal food shop in central Greece belonging to one of its lawmakers.
Fissas`s killing has led to an investigation into the party for evidence linking it to the attack and dozens more criminal offences. It has also prompted a shake-up of Greek police following reports that Golden Dawn party cells were operating within the force.
A senior court official told reporters on Wednesday that prosecutors investigating Golden Dawn had found evidence that could help them establish whether it is a criminal organization.
Citing fingerprint and photographic evidence, the official - who spoke on condition of anonymity - said that at least one person linked with the party has taken part in two separate gang attacks against political opponents and immigrants.
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