A standoff between authorities and members of the extremist far-right Golden Dawn party in Athens over food handouts degenerated into violence as the mayor was assaulted by a reportedly armed Golden Dawn MP.

Mayor Giorgos Kaminis said that MP Giorgos Germenis tried to punch him and attempted to draw a gun at a charity food distribution centre in the Greek capital.

"This man sneaked in, we didn't notice him and he tried to hit me," Kaminis told Vima FM radio. "At the last minute my personal guards stopped him."

Germenis' punch missed Kaminis and struck a 12-year-old girl, local media reported. Germenis then tried to pull a gun but was blocked in time, the mayor said. The girl suffered a bruised forehead, local media reported.

Video footage uploaded on YouTube shows security guards trying to contain Germenis.

The mayor recently banned Golden Dawn members from staging a "Greeks-only" handout of traditional Orthodox Easter food, such as lamb and eggs, ahead of Sunday celebrations in Athens' central Syntagma Square.

In defiance of the ban, 40 Golden Down members wearing traditional black T-shirts started distributing bags of food in the square after checking recipients' identity cards.

Police intervened and fired teargas. A brief scuffle broke out, as authorities prevented the Golden Dawn truck from unloading its cargo of meat and other goods.

Golden Down resumed the handouts at the party headquarters near Larissis train station in central Athens and Kaminis was confronted as he visited a municipal food distribution centre nearby.

"The only thing these people know is the language of violence," Kaminis said.

"Syntagma Square will never be used again by anyone to hand out goods," he told Skai TV. "Thuggery will not prevail in this city as long as I am mayor."

Germenis is one of the 18 Golden Dawn MPs who won a seat in parliament in the 2012 elections.

The extremists have been channelling the unrest caused by the country's deep economic crisis into blaming the large immigrant population.

An April report by the Council of Europe said: "The steep increase in hate crimes in Greece, primarily targeting migrants, is an issue of grave concern," and urged authorities to take prompt action.

Human rights commissioner Nils Muiznieks blamed a number of the attacks on Golden Dawn, which he described as a "neo-Nazi and violent political party". He suggested that the government should ban the movement.