The move was welcomed by their opposition partners, the Left party and the Green party, who have long been advocates of "individualized" parental leave.
Swedish parents currently share 13 months of parental leave. Two of these months are reserved for the mother, two for the father and the remaining nine can be disposed as the two parents see fit.
The Social Democrats now want to limit parents freedom to transfer parental leave days to one another in a first stage to their proposal.
"We have been known the world over for a family policy with a clear equal opportunities profile. But it is time for an upgrade," said Ylva Johansson of the Social Democrats to Svenska Dagbladet.
Johansson, together with Swedish metalworker's union leader, Stefan Löfvén, leads the party's counsel for the development of its future welfare policy.
As late as 2005 the Social Democrat party congress rejected calls for more earmarked months.
Opposition partners, the Green and Left parties, have welcomed the declaration from the Social Democrats.
"A positive message and a step in the right direction, even if they have not fully supported a completely shared parental leave. But if feels like they are on the right track," said Left party leader Lars Ohly to news agency TT.