Thousands of Greeks have taken to the streets to denounce the murder of a rap musician stabbed to death by a member of the far-right Golden Dawn as a government inquiry presented evidence of widespread infiltration of security forces by the ultra-nationalist party.

The organisation has denied any involvement in the killing of Pavlos Fyssas and the party's leader, Nikos Michaloliakos, warned that what he described as mud-slinging and slander "would open the gates of hell".

Golden Dawn, whose emblem resembles the swastika, said the media was behind a "dirty war" to annihilate it and singled out the Guardian – "the newspaper of capitalists in the City" – for inciting violence against the group. "[All of which] proves, exactly, the role of certain embassies in the entire operation to dismantle [Golden Dawn]," it said.

The statement was posted on the party's website after a survey by the polling company Alco showed support for the group dropping by four percentage points, from 10.8%, in the wake of the fatal stabbing.

The overwhelming majority of respondents blamed Golden Dawn – whose meteoric rise on the back of economic discontent has made it Greece's third-largest party – for the escalating violence.

Last week's killing not only convulsed Greek society but prompted a number of former Golden Dawn sympathisers and cadres to break their silence. The picture that has emerged is of an organisation run as a chain of cells with a strict chain of command leading all the way up to Michaloliakos, a mathematician who founded the party more than 20 years ago.

Members have spoken of collusion with the police – who in one video are seen giving cover to Golden Dawn supporters during street battles against anti-fascists – and special forces from whom they have claimed to have received training in clandestine camps.

Stepping up investigations into whether Golden dawn acted as "a criminal neo-Nazi" organisation, judicial authorities have signalled that at least five more party cadres will be charged in connection with Fyssas's murder.

Public order minister Nikos Dendias, who ordered the probe into Golden Dawn, said he had sent further evidence of the extremists' complicity in attacks on immigrants, leftists and trade unionists to Greece's supreme court. The file chronicles more than 150 incidents in a dossier of violence dating back to 1992. It comes in addition to human rights groups linking the neo-fascist party to over 300 assaults, mostly on dark-skinned migrants, in the three years since debt-stricken Greece descended into economic crisis.

Antonis Samaras' fragile coalition has pledged to cut off state funding to the party if it is found to be connected to the murder. Golden Dawn has vehemently denied any involvement in the crime, despite the man who has confessed to the killing claiming allegiance to the group.

Greece has come under heavy pressure from Brussels to clamp down on the openly racist party, with several MEPs and other officials expressing doubt over whether the country should be allowed to assume the rotating presidency of the EU in January if it fails to do so.