A top aide to Greek prime minister Antonis Samaras has resigned following the outcry caused by a video released by the neo-Nazi Golden Dawn party showing him in a friendly conversation with Golden Dawn MP Ilias Kasidiaris over the party crackdown.

Panayiotis Baltakos, cabinet secretary to Samaras, has apologised for the comments, which he said were intended to "relieve pressure" from Golden Dawn party officials, according to AP.

In the undated video, Baltakos can be heard saying that there was no evidence to support the government's crackdown on the neo-Nazi party, which followed the fatal stabbing of left-wing hip-hop singer Pavlos Fyssas by a Golden Dawn supporter last year.

The PM's top aide admitted that the prosecution was mainly political and aimed at stopping the far right party drawing support from New Democracy.

"They left you out of prison for so long as they didn't have evidence," Baltakos allegedly said in the video, according to a translation by Greek Reporter.

He added that justice minister Haralambos Athanassiou and Interior Minister Nikos Dendias used their influence on the supreme court's chief prosecutor to convince her that Golden Dawn were "pagans, idolaters, Nazis and opposed to Christianity".

Transcripts of the video were released by Golden Dawn spokesman Ilias Kasidiaris while footage of the meeting was uploaded to a Russian file-sharing website and YouTube.

Baltakos was appointed cabinet secretary in June 2012, and is being identified with the right-wing section of new Democracy. He reportedly opposed the crackdown on the neo-Nazi Golden Dawn party. He said that a crackdown "would backfire, winning the party sympathy from voters disgusted with the establishment and alienating conservative constituencies such as the army and church", according to the Wall Street Journal,

In 2013 he said that cooperation between New Democracy and Golden Dawn in future elections was "undesirable but not an unlikely possibility".

On Wednesday, Greece's parliament agreed to lift the immunity of a further five Golden Dawn lawmakers, paving the way for prosecutors to file criminal charges against them.

The probe into the alleged criminal activities of the far-right group was triggered by the murder of anti-fascist rapper Pavlos Fyssas, nicknamed Killah P. Among those awaiting trial is the party leader, Nikos Michaloliakos.

Golden Dawn has always denied any role in the killing of Fyssas. Police arrested a 45-year-old self-professed supporter of Golden Dawn, George Roupakias, over the murder.

Greek prosecutors have linked Golden Dawn with a series of violent attacks mostly against immigrants but also against political rivals.

Six of the party's lawmakers are in pretrial detention. Another three, including party spokesman Ilias Kasidiaris, are also awaiting trial on the same charge but are not being held in custody.

Golden Dawn won 18 seats in the 300-strong Greek parliament after national elections in June 2012, gaining support amid Greece's economic crisis and growing unemployment.

Last year its support peaked to 15%, becoming the third most popular party in Greece. Since then, the backing for the party has dropped to around 7%.