The report, which seeks to modernise parental leave provisions throughout the European Union, also calls on national governments to introduce high-quality, accessible childcare facilities.
Conservative MEPs voted against the report in committee.
Neena Gill MEP said:
"These measures will introduce an element of gender equality and fairness by introducing much needed facilities to allow for the better sharing of family tasks between men and women.
"This directive seeks to give women a much improved capacity to participate in the job market on more equal terms. The outdated view that bringing up children should be the sole responsibility of mothers is holding back progress for gender equality. The old rules were taking women out of the labour market and not letting men have the chance to be fathers.
"The full implementation of the parental leave directive will give hundreds of thousands of fathers the ability to spend quality time with their new children after birth.
"Thanks to our EU membership, parents already have the right to maternity and parental leave - guaranteed paternity leave would help fathers to spend even more quality time with their newborn children."