More than 54,400 valid signatures were deposited this week for the national referendum opposing the two-week paternal leave, the Federal Chancellery announced.
A minimum of 50,000 signatures are needed for a referendum to go ahead.
Voting will likely take place in September.
The measure was sponsored by the right-wing Swiss People’s Party, some members of the Liberals, and Christian Democrats. They claim that the proposal adopted by the parliament last year, granting fathers a two-week leave, would be too expensive, with employers and employees sharing the extra costs.
The financial burden would amount to 230 million francs per year and would require an increase of 0.05 points in the social contributions, the referendum’s sponsors say.
Paternity leave has been fueling political debates in Switzerland for years, with the parliament repeatedly turning down various proposals that called for a four-week leave.
Last September deputies finally backed the one calling for a two-week leave, seeing it as a compromise in the face of the four-week proposal developed by the trade union Travail.Suisse.
Mothers in Switzerland receive 14 weeks' leave at 80 percent pay, up to a maximum of 196 francs a day.
Overall, Switzerland rates poorly in comparison with other European nations when it comes to parental leave.
According to a report by the United Nations Children’s Fund (UNICEF), Sweden, Norway, and Iceland have best family-friendly policies among 31 rich countries, while Switzerland, United Kingdom, and Ireland rank the lowest.