Politicians in the upper house voted 29 to 7 against the proposal which had narrowly passed through the lower house Council of States.
The motion had been put forward by Lorenzo Quadri, a senator for the right-wing Ticino League party in Switzerland's Italian-speaking canton of Ticino.
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The proposal, modelled on rules already in place in Austria, would also have seen imams required to preach in a Swiss national language while compelling Islamic centres to disclose the origin of any funding.
With the motion, Quadri had targeted some 35 mosques and Islamic centres in Switzerland reportedly funded by the Turkish government with the money being used to spread radical Islam, Swiss news portal 20 Minuten reported.
But Switzerland's seven-member Federal Council had said the motion was discriminatory and rejected the comparison with Austria saying rules in that country came in the context of bolstered official recognition for Austria's Muslims.
The Swiss executive noted, however, that no Swiss canton had officially recognised Islam and it was unfair to impose rules without offering rights. Green senator Robert Cramer also noted the motion could impinge on religious freedoms and the right to free assembly.
A Swiss Islam?
The Swiss Socialist Party (SP) demanded in a recent strategy paper that Islam be recognised officially in Switzerland as long as equality between sexes was guaranteed, the secular state was recognised, financial transparency was assured, and independence from foreign countries existed.
In return, Islamic communities should have the right to collect taxes like the official churches in Switzerland as well as to provide pastoral care in prisons, hospitals and the army.
"We need a Swiss Islam," said SP president Christian Levrat of the plan set to be discussed at an upcoming party summit.