Swedish Prime Minister and Social Democratic Party leader Stefan Lofven (C) arrives for a news conference after meeting with the Speaker of Parliament in Stockholm. Picture: TT News Agency/Pontus Lundahl via Reuters

Stockholm - Sweden's anti-immigration party - which is shunned by the political mainstream - insisted on Thursday it would block the formation of a new government unless it gets a say in policy - something the two main political blocs have ruled out.

The Sweden Democrats have grown in popularity since entering parliament in 2010 and hold the balance of power after winning 62 seats in the 349-member house at a Sept. 9 election.

They voted with the centre-right Alliance bloc to scupper the government of Social Democrat prime minister Stefan Lofven on Tuesday. But at consultations on forming a new administration on Thursday, said they would not back an Alliance government.

"We will not, either actively or passively, support a government that does not give us influence," Sweden Democrats leader Jimmie Akesson told reporters.

The speaker of parliament has four attempts at picking a prime minister who can get support from parliament - a process that could take weeks. If he fails there will be a new election within three months.

Lofven and Alliance leader Ulf Kristersson are both claiming the right to build a new minority administration.

Kristersson said he wanted to form a government consisting of his Moderate party and its Centre, Liberal and Christian Democrat allies. With 143 members of parliament, that grouping is one seat smaller than Lofven's centre-left bloc.

Lofven, whose Social Democrats are the biggest party in parliament, is hoping that the Centre and Liberal parties will support him if their only other option is a deal with the Social Democrats.

The speaker will hold a news conference later in the day after completing his first round of talks with all the party leaders.