Last autumn, the government agreed with the four centre-right parties in the opposition on a range of policies to try to stem the flow of refugees coming to Sweden. Some of the policies were also aimed at trying to help newcomers integrate here.
One concern was that women arriving with young children would end up taking a lot of parental leave and therefore increase their problems of getting onto the Swedish labour market. This resulted in an agreement to limit the parental leave of people who come to Sweden with children.
The plan was that immigrants would only be able to use a "limited number" of parental leave days after the child's second birthday. For people who have given birth in Sweden, there is no equivalent of this; they only need to make sure they take out a majority of the parental leave before the child is four years old.
"There may be benefits in that women born abroad would faster establish themselves on the labour market, and also that the children would get in touch with Swedish pre-schools much faster, which also can be important for the language development," said Social Insurance Minister Annika Strandhäll in an interview with Swedish Radio.
Having said that, Strandhäll still would like to analyse the issue further before putting forward a bill on the matter. She refers to the already ongoing review of the parental leave system that the government has commissioned.
"The inquiry into the whole of the parental leave insurance is also looking into this. Is it possible to introduce such a distinction in the parental leave insurance and what would the consequences be? Before we have the result of the inquiry on the table it is difficult to say either yay or nay to this," she says.
And she notes that it may not be possible to have a separate set of rules for one group in society.
"That would be something very new to Sweden," she says, adding that it is hard to tell whether it is in fact possible to make such an exception.
And one of the experts in this inquiry, Joa Bergold from the trade union federation, is very critical of the idea that one should make special parental leave rules for immigrants.
"We find it very problematic to separate certain groups that have less right to parental leave the way it looks today. We will never accept a separate solution just for certain groups," she tells Swedish Radio.
But Johan Forsell, of the conservative Moderate Party, which agreed with the government on this deal, says it is very important to limit the right to parental leave for immigrants as the current system risks becoming a trap for women.
"This is part of a deal that we cut with the government, so I am taking it for granted that the government also will carry it out," he says.
Asked how far it is possible to have separate rules for new immigrants and for others when it comes to the parental leave, Forssell says "this objection has not been brought up before, when we made the deal with the government, so I assume that they will find a solution to it. This must be implemented, we have a very difficult situation when it comes to integration in Sweden".
The inquiry into the parental leave system will present an interim report this autumn, but the final results will not be done until October 2017.