The law will compensate grandparents for caring for their children's newborns in certain situations, such as when young parents need at least two more years to complete their education. This and other situations where the parents can prove they need their own parents to support them in raising their children will be considered for the government benefits.
The new law is subject to approval by the upper house of parliament, the Bundesrat, in December.
Germany has one of Europe's lowest birthrates, but the German Family Ministry has reported that it increased slightly to 1.4 children per woman last year to reach its highest level in 17 years. Chancellor Angela Merkel has named the shrinking population as one of the country's most pressing problems and pledged to make it easier for parents to combine a career and having children.
Nearly one-fifth of German fathers have taken advantage of the country's parental leave benefits, which allow them to stay home on two-thirds of their pay for a year.