The initiative ‘For a reasonable paternity leave – in favour of all the family' was launched a year ago by four organizations: labour group Travail Suisse, feminist umbrella organization Alliance F, men's group männer.ch and Pro Familia Suisse.
On Saturday Travail Suisse said the initiative had gathered 120,000 signatures, more than enough to push it to a public vote.
The initiative calls for fathers in Switzerland to get 20 days statutory paternity leave to take in a flexible manner within the first year of their baby's life.
It would be financed through the system of deductions used to finance maternity and other kinds of leave, such as military service.
Switzerland currently has no statutory paternity leave, with most fathers only allowed to take one ‘family day' of leave upon the birth of their child.
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A 2015 report by Travail Suisse found that more than half of workers employed in the private sector only get one day off after a child is born.
Some companies do offer more, but the report found that only three percent of fathers were eligible for more than ten days paternity leave.
Parliament has frequently rejected calls to legislate for increased paternity leave, since the idea is not supported by the political right who feel it's not necessary to legislate on the matter at federal level.
In a statement, Travail Suisse said the idea of paternity leave had been rejected by parliament 30 times in the past decade.
According to a 2015 survey undertaken by the group, more than 80 percent of Swiss voters would be favourable to the idea of paternity leave.
“A single day of paternity leave no longer meets the needs of families today,” said the group.
“The model of 20 days with flexibility is a reasonable solution and therefore typically Swiss.”
As well as being good for families, it is good for managers too, since it allows fathers to negotiate with their workplace to find a suitable time to take paternity leave that works for both parties, it added.
Statutory paternity leave would also level the playing field between large companies – some of which already have the means to offer increased paternity leave – and small businesses, which do not.
Hailing the success of the initiative so far, its campaign director and Travail Suisse president Adrian Wüthrich said he was “proud” to be able to lodge this initiative for paternity leave after just one year of campaigning.
The signatures will be registered with the federal chancellery this summer.
If declared valid, the initiative would then be put to the Swiss public in a referendum.
Under Switzerland's system of direct democracy, anyone can create a so-called popular initiative which must gather 100,000 signatures within 18 months in order to push it to a referendum.
Switzerland currently lags behind other European countries on the issue of paternity leave.
The EU average is 12.5 days, though some countries such as Sweden allow far more through shared parental leave policies.
Mothers in Switzerland are entitled to 14 weeks paid maternity leave.