SWEDISH police say they hope reinforcements will help quash nightly riots that started nearly a week ago in Stockholm's immigrant-dominated suburbs and have spread.

"With the strong presence on the streets of the good forces, and the police reinforcements, I think we are well on our way towards calmer times in the coming days," Stockholm police spokesman Kjell Lindgren said on Saturday.

Cars and buildings were torched overnight on Friday to Saturday in the towns of Oerebro, Uppsala and Linkoeping, though tensions showed signs of easing in Stockholm's suburbs.

The unrest has sparked debate among Swedes over the integration of immigrants, many of whom arrived under the country's generous asylum policies, and who now make up about 15 per cent of the population.

Firefighters responded to about 30 or 40 incidents in the greater Stockholm area overnight, down from 70 the night before and 90 the night prior to that.

"The past night was the calmest we've seen so far," Lindgren said, adding police reported no incidents of stone throwing or clashes with troublemakers.

Police reinforcements arrived on Friday from Sweden's second and third biggest cities, Gothenburg and Malmo - which have both experienced riots in recent years - and volunteers patrolling the streets to restore calm had had a deterring effect and helped reduce the violence, Lindgren said.

Police have refrained from clashing with troublemakers during the almost week-long riots. Only a handful or injuries have been reported, most among police officers attacked with rocks.

Sweden's opposition Social Democratic party leader Stefan Loefven, who recently visited the Husby suburb where the troubles began on May 19, attributed the unrest to long-term unemployment in the affected areas and a widening gap between rich and poor.

"The most important thing is to understand the causes for what is happening and everyone I spoke to (in Husby) said the same thing: jobs and education," he told Swedish Radio.

"The political message is important now, that society is here for you. You have to take responsibility, conduct yourself well, go to school and not torch cars. But we will help you," he said.

Official data show unemployment was 8.8 per cent in Husby in 2012, compared to 3.3 per cent in Stockholm as a whole.

Due to its liberal immigration policy, Sweden has in recent decades become one of Europe's top destinations for immigrants and asylum seekers, both in absolute numbers and relative to its size.

But many of them struggle to learn the language and find employment, despite numerous government programs.

According to the OECD, Sweden still ranks among the nine most equal member states of the organisation which includes the world's leading economies.

But inequality surged by one third between 1985 and 2008 - the largest among all OECD countries, the organisation said in a report earlier this year.

In addition, the disappearance of many low-skill jobs in Sweden's high-cost economy has made it harder for many immigrants to get a foothold, experts argue.