"We cannot agree to an application to ban [the party]," said FDP leader Philipp Rösler on Monday and added that his liberal-leaning party had always been against a ban. "You can't put a ban on stupidity," he said.
His words drew sharp criticism from the Central Council of Jews in Germany, which accused Rösler of downplaying the danger from the far-right National Democratic Party (NPD).
"It's a disastrous and wrong move on the part of the FDP," president of the council Dieter Graumann told the Handelsblatt newspaper on Monday.
A potential ban on the party was about preventing tax money going to finance "hate," said Graumann and said that with their "signal of political indecision" the FDP had put a de facto block on the ban.
The last attempt in 2003 by the then government to outlaw the NPD failed after legal complications arose from the presence of state intelligence agents in the party ranks.
This latest anti-NPD initiative originated in the Bundesrat upper house of parliament last year, prompted by the discovery in November 2011 of a far-right terrorist cell believed to be behind a murder spree stretching back seven years, in which most of the 10 victims were immigrant shopkeepers.
Last December representatives from Germany's 16 states voted unanimously, bar one abstention, to ask the country's highest constitutional court to ban the party on the grounds that it sought to undermine the national constitution.
Yet high-ranking politicians including Chancellor Angela Merkel and Interior Minister Hans-Peter Friedrich have raised doubts about whether a ban would hold up in court.
All five of Chancellor Merkel's FDP cabinet ministers, including Economics Minister Rösler, said they would not support the ban on Monday, meaning the governing coalition as a whole was now unlikely to back the legally contentious move.
Merkel has said she would be seeking a unanimous decision within her cabinet when it met to discuss the ban on Wednesday.
The lower house of parliament, the Bundestag, has also not yet indicated whether it will support the states' initiative, but without government backing, the attempt to ban the fringe neo-Nazi party could find itself on much shakier legal ground.