Senators have voted against the right-wing cabinet’s plan to invoke crisis legislation to reduce refugee numbers, in a major blow to government strategy.

The coalition does not have majority support in the upper house of parliament and most of the opposition, including fundamentalist Protestant party SGP, voted for a motion describing the crisis plan as “undesirable”. The motion also called on the government to come up with a “plan B”.

Ministers can invoke crisis legislation without the green light from either house of parliament, although MPs and senators will have to approve any measures that stem from the move retroactively.

Senators say the cabinet’s wish to toughen up legislation to reduce refugee numbers can be achieved using other methods, such as fast-track legislation which does not bypass parliament.

PVV leader Geert Wilders has said repeatedly that the coalition will be in trouble if crisis legislation is not invoked. Migration minister Marjolein Faber is currently working on the legal justification for the move, which is due to be presented before October 25.

Prime minister Dick Schoof described the senate vote as an “important signal” which would be “taken into consideration”.