Two years ago, a law came into force requiring immigrants to have a job and somewhere to live before applying to have their families follow them to Sweden.
In 2011, 366 applications by immigrants to join a family member in Sweden were rejected because the person in question was not working.
By 2011, less than half that number were rejected, reports political newspaper Riksdag & Department (RoD) after looking at Migration Board">Migration Board (Migrationsverket) figures, something which doesn't sit well with Billström.
”Far too few people are subjected to this requirement if you look at it in relation to the large number of people who come to Sweden through family reunification," he told Sveriges Radio (SR).
"That’s why the self-sufficiency requirement should be thoroughly examined."
Prime Minister Fredrik Reinfeldt stood behind his minister on Monday.
“Tobias Billström feels that exceptions to the law have become too widespread,” Reinfeldt told the TT news agency.
But other members of the government coalition think the exceptions were made for good reason.
“People who are issued an exception to the rules are mostly minors. They have been living in the very situation from which their parents fled,” Christian Democrat MP Emma Henriksson, who sits on the parliamentary committee on social security, told TT.
"We’re talking about Somalia but also Syria.
"It is important to us that we don’t propagate policies that keep families apart. Parents and children should be together.”
The government says the law was meant to provide an incentive for immigrants to find work, a claim Reinfeldt reiterated on Monday.
"We think it’s important that immigrants are included in our labour policy. It is also a way for Sweden to prepare for the many relatives we are expecting,” said Reinfeldt.
Earlier this year, Sweden scrapped a requirement that Somali immigrants show documentation to prove family ties. The government instead opened the door for DNA testing.
"Somalis are one example,” Reinfeldt said.
"But in general this is related to our high level of asylum seekers. And it will apply to unaccompanied refugee minors who at a later date want their families to follow.”
The prime minister seemed aware that his Billström might face some opposition for his call to make it hard to claim an exception to self-sufficiency requirements.
“We have to discuss this with our coalition partners and also, further on, with the Green Party,” Reinfeldt told the TT news agency.
After the last election, the centre-right Alliance government struck a deal with the opposition Green Party on immigration policy
The agreement was a way to exclude the anti-immigration Sweden Democrats from having any chance to vote against the minority government in parliament on issues related to immigration policy.
The deal with the Green Party has already forced the government to make certain compromises.
Green Party migration policy spokeswoman Maria Ferm said on Monday that her party would not get involved in changing the current reunification rules.
“It is a human right to be reunited with your family if you have escaped war or conflict,” she told TT.
She also said the proposal could damage Sweden’s efforts to help newly-arrived immigrants integrate.
"It’s counter-productive. If people have to worry constantly about their family and whether they are alive or dead, it is difficult to get into a new society, learn a new language and find a job," said Ferm.