A spokesman said a regularisation of status similar to that in neighbouring countries could end a political stalemate.
He said the situation for rejected asylum seekers and other foreigners without permits had worsened over the past four years.
In a meeting with Justice Minister Simonetta Sommaruga on Tuesday a delegation asked her for assurances that the 173 people listed would not be deported.
However, it did not receive any promises, according to a government official.
Similar moves, including a formal petition calling for the legalisation of an estimated 100,000 illegal immigrants in Switzerland, have been made over the past two years.
In the past supporters also occupied the headquarters of the Social Democratic Party in Bern calling on the centre-left group to put the issue higher on its agenda.
In 2000-2001 support groups occupied several churches as part of public protests.
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Petition to help illegal immigrants handed in
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Sanchez, now 41, managed to live in Switzerland illegally for 14 years before she received a much-desired residence permit three months ago after applying as a hardship case. “This residence permit is the best gift ever – I can still hardly believe my luck,” Sanchez* tells swissinfo.ch, her eyes shining. Yet the old fear of…
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If you want to start a conversation about a topic raised in this article or want to report factual errors, email us at english@swissinfo.ch.