Fearing another court defeat, Chancellor Angela Merkel's government did not formally back the petition to the Constitutional Court to ban the NPD, which the domestic intelligence service has called "racist, anti-Semitic and revisionist".
Banning a political group is difficult in Germany, still haunted by memories of Nazi and communist regimes which crushed dissent. A previous attempt in 2003 to ban the NPD failed.
Germany's Turkish community, the Central Council of Jews and Central Council of Sinti and Roma have criticised the government for failing to join the states in their petition.
Calls to ban the party grew after it emerged in 2011 that a neo-Nazi cell had gone on a killing spree. The NPD denied any links to that.