The Association for a Tolerant and Open-minded Switzerland said the petition was a sign of solidarity with Muslims in Switzerland.
The signatures, collected mainly via the internet, were handed over to a Muslim youth organisation, Ummah, in Zurich on Saturday.
Nearly 58 per cent of voters in November approved a proposal by the rightwing and ultra-conservative parties to ban the construction of minarets.
The result is seen as a major upset for the government and parliament and prompted a public outcry.
On Thursday the United Nations Human Rights Council narrowly passed a resolution condemning defamation of religion, which included reference to “Islamophobic” bans on building new minarets on mosques.
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