The initiative ‘For a reasonable paternity leave – in favour of all the family' was launched by labour groups and family associations on Tuesday after the text was approved by the federal chancellery.
They now have until November 2017 to gather the 100,000 signatures required to put to it the public vote.
The initiative demands that fathers in Switzerland be entitled to least four weeks (or 20 days) paid paternity leave by law, to be taken at any time during the first year following the child's birth.
It would be funded under the same welfare system that pays mothers on maternity leave and men taking leave from work for military service.
Currently there is no statutory paternity leave in Switzerland, though fathers are entitled to take one or two ‘family days' for the birth of their child.
Some Swiss companies grant fathers more than that, although a 2015 report by labour group Travail Suisse revealed that 52 percent of male workers in the private sector were eligible for just a single day's paternity leave, and only three percent were entitled to take more than ten days.
The issue has long been on the political agenda in Switzerland, with parliament rejecting the idea numerous times.
Most recently, at the end of April the lower house voted against a motion proposing two weeks statutory leave for fathers, with opponents saying the government shouldn't “intervene” on the issue.
Backing the new initiative, Travail Suisse said in a statement that parliament had rejected the idea 30 times.
“But the people have a different opinion on the subject: 80 percent of voters want paternity leave,” it said.
“The theme of paternity leave shows the large gulf which exists between the politicians and the people.”
It's for that reason some 140 organizations have rallied behind the creation of a popular initiative, it said.
“The positive effects of early fatherly involvement are proven. The bond with the baby is stronger and the development of the child is more intensive,” said the group.
“Children whose fathers are involved early have better social skills, succeed better at school and are more physically robust.”
Paternity leave would also benefit mothers, it added, by supporting their return to work and allowing them to better balance family and professional commitments.
Introducing statutory paternity leave would cost the economy, per person, the equivalent of “no more than a cup of coffee a month,” it argued.
Switzerland lags behind other European countries on the issue.
Paternity leave across the EU averages at 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.