"The NDP is a party that is an enemy of the constitution. We want to start a process to ban it," said Hans-Peter Friedrich, federal minister of the interior, on Thursday after his regional colleagues met.
Germany was last year rocked by the revelation that a fascist gang, calling itself the National Socialist Underground based in the eastern town of Zwickau, was made up of people close to the NPD.
The cell has been accused of at least 10 murders between 2000 and 2006, mainly of Turks.
The NPD was established in 1964 and garnered 1.5 percent of the vote at the last federal elections in 2009. It has never had a seat in the Bundestag, the lower chamber of parliament.
The party has a strong presence in the former East Germany.
Previous attempts to ban it failed after it emerged that NPD leaders upon whose anti-constitutional statements were used as evidence against the party, were being paid by intelligence agencies.
Some moves have been made regionally to shut down such informants in the hope of clearing the decks for another attempt to ban the party.