The cabinet of Chancellor Gerhard Schroeder had already decided to ask the country's Constitutional Court to outlaw the party, which it holds responsible for inciting attacks against foreigners which have left six people dead this year.
The court could have acted on the application of the cabinet alone, but Mr Schroeder said he wanted to present a united front of cabinet and both houses of Parliament.
The Bundesrat debate came the day after 200,000 people rallied in Berlin to protest against racism.
Conflicting signs
Leading politicians, including Chancellor Schroeder and President Johannes Rau, joined Jewish leaders, opposition figures and celebrities such as tennis star Steffi Graf for the march, which the chancellor called a "revolt of the decent".
But just a day before the march, the e-mail address of a group of Jewish students in Germany was flooded with more than 17,000 messages threatening to repeat the Holocaust, the Associated Press reported.
The e-mails reportedly originated from a server in the United States, making it impossible for German police to investigate the incident as a violation of German anti-hate crime laws.
Lower house dissents
Despite the Bundesrat decision to back the NPD ban, Germany's lower house, the Bundestag, may not debate the issue at all.
Some parties, including the small liberal group the Free Democrats, say the evidence against the NPD is weak.
They apparently fear that a failed attempt to ban the party would, in effect, give the NPD a clean bill of health.
The Constitutional Court is expected to give some feedback on the merit of the application to ban the NPD before Christmas, but an actual legal ruling could easily take years.
Tiny party
The NPD, a fringe party with just 6,000 members, favours policies benefiting ethnic Germans and an end to new immigration.
It has become associated in recent years with young skinheads.
To make the ban effective, the government must show the constitutional court that the NPD poses a threat to democracy in Germany.
Only two political parties have been banned in post-war Germany.
The successor to the Nazi Party was outlawed immediately after the war, and the Communist Party was banned in West Germany in the 1950s.
About a dozen other organisations have been outlawed, including the far-right Hamburgersturm (Hamburg Attack) and the British-based Blood and Honour group.