On Tuesday, the parliamentary chamber voted down the funding for a second time, despite the requested amount being reduced to CHF66.5 million.
The House of Representatives supports the funding that cannot be released until both chambers agree.
In instances where parliamentary chambers cannot agree on funding matters, the decision that involves less public outlay takes precedent.
Cantons wanted the money to fit out new refugee centres, having exhausted all the facilities that were offered by the army.
Last year Switzerland registered 24,500 asylum-seekers, which was 64% more than the previous year. This excludes some 75,000 Ukrainian refugees, who received a special protection status through an accelerated registration process.
Refugee numbers this year are estimated anywhere between 27,000 and 40,000.
The situation has been made worse by an Italian decision to maintain a ban on re-admission of refugees from neighbouring countries that it imposed in December.
This prevents Switzerland from sending refugees back to Italy.
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