Asylum seekers fleeing Iraq and Syria are straining Sweden's public finances just as the government is likely to cut its estimate for economic growth next year, Finance Minister Anders Borg said.

Sweden's asylum policy is one of the most generous in Europe. As the costs mount, a populist anti-immigrant party, the Sweden Democrats, has risen in opinion polls before a general election in September.

In the first seven months of this year, 41,303 people sought asylum in Sweden, according to the Swedish Migration Board, an 80 percent increase over the same period last year, with the biggest increase from Syria.

"The developments in Iraq and Syria mean that we have a rather substantial increase in costs for asylum, integration and migration. This will have an impact on the public finances," Borg told reporters.

"It involves substantial amounts in billions (of Swedish crowns) that will also accumulate over the years," he added, saying authorities were working on estimates of how much this would cost.

"Those are cost increases for 2014 and 2015 which then will accumulate to rather substantial effects going forward, but we are still working with this."

Earlier this year, the government estimated the cost of receiving asylum seekers would jump to 7.0 billion Swedish crowns ($1.0 billion) in 2014, up from 5.1 billion crowns in 2013.

According to Sweden's Migration Board, around 40,000 people have sought asylum from Syria since conflict started in 2011.