STOCKHOLM (Reuters) - The head of the far right Sweden Democrats said he aimed to win a quarter of voters at a 2018 election with a call for a total ban on new asylum seekers and saw signs mainstream parties may be seeking the party’s backing in parliament.

Jimmie Akesson’s party has gained support over the last decade, rising from a fringe group with neo-Nazi roots to win 13 percent in 2014’s election and hold the balance of power in parliament. Polls now give it about 17 percent.

Its growth echoes that of populist parties in the Nordics, which either support or form a part of government in neighbours Norway and Denmark. But Sweden’s political mainstream has so far shunned the Sweden Democrats due to their radical roots.

That may change, said Akesson, who has purged the party of its more militant elements and whom many credit with making the Sweden Democrats respectable in the eyes of thousands of voters worried about declining schools, doctor shortages and rising crime figures.

Last year’s migrant crisis also boosted far right parties across Europe.

“It will be hard to shut us out. We could even be the biggest party after the election,” Akesson said.

Akesson is part of a European backlash. An anti-Islam party leads polls in the Netherlands while the National Front’s Marine Le Pen is strongly placed for presidential elections in April.

A foothold in government for the party would mark a watershed in a country where generous asylum policies have until last year commanded automatic support across the political spectrum.

Akesson said his party did not have to be a formal party of government, but wanted to put its stamp on key policy areas: immigration, law and order and the welfare state.

“I don’t care so much about portfolios or (ministerial) posts,” he said. “For me it is the core policy that matters.”

SOFTER TONE?

Flanked in his office by a photo of the Swedish royal family and of rock band Kiss, Akesson said he expected the party to get 20-25 percent of the vote in 2018.

That would put it on an equal footing with the centre-left Social Democrats - the larger party in the current minority coalition - and the Moderates, the biggest centre-right group and part of the four-party Alliance opposition bloc.

“The main scenario for me is that we build a government together with the Moderates and the(centre right) Christian Democrats,” Akesson said.

The 2015 migrant crisis which saw 160,000 people seek asylum in Sweden has hardened voters’ attitudes.

Tough asylum rules introduced late last year by a hard-pressed minority centre-left coalition have cut applications to around 20,000 so far this year.

“We are still the party which has most credibility in immigration policy,” Akesson said. “The other parties have confirmed our views. We were right and the voters see that.”

Neither the centre right nor the centre left parties can form a majority government without the support of the Sweden Democrats. Their refusal so far to treat with the far right has led to some degree of parliamentary stalemate.

But Akesson sees signs that is changing. Earlier this month, the leader of the small, centre-right Liberal Party called for the Sweden Democrats to be allowed to take part in cross-party discussions led by the government.

The leader of the Christian Democrats - also part of the centre right Alliance - has softened her tone. Still, the Moderate Party, the biggest centre right party, has said cooperation is not on the cards.

“The signal we get from ... the centre-right parties is that they are ready in some form or another, to get our support in order to form a government,” Akesson said.

Some political analysts say Akesson ambitions may bear fruit.

“The most likely scenario after the election is some sort of understanding between the Moderates and the Sweden Democrats with the Christian Democrats tagging along,” said Nick Aylott, political science professor at Sodertorn University.

Cooperation would have a price.

Akesson said more asylum seekers should be turned around at Sweden’s borders and there should be tougher rules for family reunions.

“Our vision is a goal of zero for asylum-based immigration,” he said.