By Balazs Koranyi and Alister Doyle

OSLO (Reuters) – An anti-immigrant populist party laid claim to a major role in oil-rich Norway‘s government for the first time on Tuesday after a center-right alliance won a landslide general election victory to oust a Labour administration.

The Progress party, which once had among its members Anders Behring Breivik, who killed 77 people in 2011 in a gun and bomb attack targeting Labour, came third in Monday’s poll, giving it a kingmaker role in coalition building.

The Conservatives, led by Erna Solberg, who won the most seats cannot form a majority government without Progress and may have to make concessions to the rightists on spending, taxes and immigration without alienating two smaller centrist parties.

“We will ensure a solid footprint in a new government and if we are going to have good solutions, all four parties must have a place, all must be visible,” Progress leader Siv Jensen said.

Progress wants to spend more of Norway’s oil wealth and curb immigration. Although it has toned down its rhetoric to court respectability, some still see it as too radical for government.

With a bumper budget surplus of 12 percent of gross domestic product thanks to hydrocarbon revenues, the new government has room to increase spending and lower the tax burden.

Solberg, a former girl scout leader who overcame dyslexia, promised to cut taxes, shrink government and improve health care but acknowledged she would have to make policy concessions.

“We will all have to give and take to get a policy stance that has a firm direction and will last over time,” Solberg, 52, said after results showed a landslide victory over Labour Prime Minister Jens Stoltenberg.

“All three (other parties) will be tough negotiators in issues close to their hearts,” she said.

Solberg will become Norway’s second female prime minister after Gro Harlem Brundtland, still considered the “mother of the nation”, and the first Conservative prime minister since 1990. At least the top two cabinet posts – and possibly the top three – are likely to go to women.

STOLTENBERG STEPS DOWN

With nearly all of the vote counted, the Conservatives, the Progress Party and two centrist parties collected 96 seats in parliament, 11 more than needed for the majority. Progress’ share of the vote actually fell. It picked up 29 seats, 12 fewer than four years ago, losing votes to more centrist parties as Norwegians shunned the extremes of the left and right.

Stoltenberg and his allies gained just 72 seats and the prime minister announced he would step down after eight years and two straight terms in office.

Norway has enjoyed rare economic success during the past decade, escaping Europe’s economic crisis with little more than a scratch, as its booming offshore oil sector lifted per capita GDP to $100,000 and a huge public sector insulated the economy.

But growth is now slowing, competitiveness is stagnating, and the government’s record on critical social services is mixed. Voters have accused outgoing Stoltenberg of wasting a once-in-a-lifetime economic boom.

The trickiest task for Solberg, who will become prime minister on her third attempt, will be to tame Progress, and woo at least one of the two centrist parties that are not keen on working with Progress.

The Christian Democrats and Liberals, one of whom will be needed for a majority, would not commit to joining cabinet but said they would ensure the center-right came to power.

“The center will play a key role,” Christian Democrat leader Knut Arild Hareide said. “We and (Liberal party chief) Trine Skei Grande have got a key role for the next four years. We are ready to put a new government in place.”

Analysts said the price of gaining the small parties’ support could include giving up plans to drill for oil in Lofoten, a picturesque archipelago in the Arctic. Energy firms have argued for the need to drill and all the big parties support their quest while the smaller parties oppose it.

SPENDING

While Solberg may have to make concessions to Progress, any shift in policy is likely to be mild, analysts said.

In immigration, Norway’s hands are tied by international treaties, which limit its room for maneuver. The economy needs new workers as unemployment is less than 3 percent and a steady influx of migrants keeps the labour market from overheating.

The next government will have more leeway on spending, as it levies a 78 percent tax on the oil sector, amassing huge budget surpluses and a $750 billion oil fund worth more than 150 percent of GDP.

Danske Bank predicted that spending under the new government would rise by up to 15 billion crowns ($2.5 billion) next year, or 0.66 percent of the non-oil economy, a big increase but well within the budget’s means.

A major sticking point will be changes to the oil fund as both the main center-right parties want big changes but they do not agree on specifics, with the Conservatives keen to get a broad consensus for any reform to the fund.

The parties are likely to find more common ground on privatization as they argue the state has grown too big. Solberg has said Norway should sell down some of its holding in Statoil and telecoms group Telenor.

Solberg said her party will meet on Friday to appoint coalition negotiators and the new cabinet will take office after the outgoing government presents the 2014 budget on October 14.

(Additional reporting by Gwladys Fouche, Joachim Dagenborg, Terje Solsvik, Henrik Stolen and Camilla Knudsen; Editing by Paul Taylor)