The chairwoman of Swedish union organisation LO, Wanja Lundby-Wedin, has demanded the previous regulations governing labour migration be restored, either under the direction of the Swedish Public Employment Service (Arbetsförmedlingen) or the Swedish National Migration Board (Migrationsverket).
However, after meeting with labour market partners, Migration Minister Tobias Billström, who has been dogged by criticism over the law over the last two weeks, insisted on Tuesday that he will not change the current law.
"What we can discuss are the terms, but not who makes the decision," said Billström.
The ruling Swedish government undertook reforms in 2008 over laws governing labour migration, granting companies more leeway in decisions over the issuance of Swedish work permits.
The labour market scrutiny involves allowing decisions to be made at the agency level to determine how much manpower is needed in the country.
Billström acknowledged that problems do exist under the reforms.
"Abusive employers have always existed and always will exist. It has nothing to do with the labour laws," he said.
The government will now look into what can be done, Billström added.
"It is the enforcement of the law that is important," he said.
Other trade union confederations have criticised the law, saying that it makes it easier for unscrupulous employees to exploit migrant workers.
Last week, Swedish trade union Unionen alleged that the law facilitates allowing Ericsson and other IT companies to attract and train foreign workers in Sweden so they can perform similar tasks in the home countries, resulting in the disappearance of Swedish jobs.
Unions have previously criticised the law for a rise in abuses against low-skilled workers such as berry pickers, the most common occupational group that receives work permits for Sweden, and other agricultural workers.