ATHENS—Greece is moving to effectively outlaw the extreme-right Golden Dawn party by asking prosecutors to declare it a criminal organization, days after police say a self-professed member confessed to killing a left-wing rap artist.

The government presented prosecutors with a legal file late Thursday that it says shows Golden Dawn acted as an organized criminal gang—a felony under Greece's penal code—and declaring it a threat to public order.

The file is based on some 30 previous cases over the past year where members or followers of the party—which is known for its extremist views and tactics against immigrants, gays and political rivals—have been charged with illegal acts,

Many Greeks identify Golden Dawn as neo-Nazi based on its rhetoric and its swastika-like emblem—a label the party rejects. It has denied any connection to the recent killing and says it condemns violence against others.