The fact that the anti-immigrant Progress Party appears to hold the key to securing a majority in Parliament has caused unease in Norway because Anders Behring Breivik, a far-right militant who massacred 77 people in 2011, was once among the party’s members.

“We will ensure a solid footprint in a new government,” the party’s leader, Siv Jensen, vowed Tuesday. After campaigning on a platform promising curbs on immigration and more leeway to tap into Norway’s oil wealth, Ms. Jensen is expected to lobby for the post of finance minister.

Norwegian voters ousted the center-left Labor Party government on Monday, choosing the Conservative Party of Ms. Solberg.

Ms. Solberg, 52, a former Girl Scout leader nicknamed Iron Erna, will be Norway’s first conservative prime minister since 1990 and its second female leader. She is expected to form a government and take office by Oct. 14, when the departing coalition of Jens Stoltenberg, the Labor Party leader, will present its last budget.

“We will give this country a new government,” Ms. Solberg said late on Monday night after Mr. Stoltenberg conceded defeat. She has said that she is prepared to form a coalition with the Progress Party, which has recently tried to tone down its anti-immigrant oratory. But convincing two other smaller center-right parties to join such a coalition might be difficult.

The campaign was centered largely on economic issues, like extending already generous welfare payments (Labor’s platform) versus cutting taxes and privatizing hospitals (the Conservative platform). But the massacre on the island of Utoya, where Mr. Breivik attacked young members of the Labor Party, many of them children, on July 22, 2011, was never far from the surface.

Mr. Stoltenberg, whose pledge after the attack for “more democracy, more openness and more humanity” won him praise at the time, saw his party’s standing decline after a commission on Norway’s preparedness for terrorist attacks reported last year that the massacre could have been avoided if security protocols had been followed properly. Thirty-three Utoya survivors ran for Labor seats and several of them lost.

The Conservative, Progress and two small center-right parties, the Christian Democrats and the Liberals, ended up with 96 seats in Parliament, 11 more than needed for a majority. Mr. Stoltenberg and his Green and Socialist allies won 72 seats.

Monday’s outcome, while perhaps puzzling to outsiders who are inevitably struck by Norway’s wealth, was broadly expected in Norway. “The wealth is also a problem for politicians,” said Bernt Aardal, professor of politics at the University of Oslo. “Every time there is a headline about health queues or deficiencies in health care for elderly people, everyone says that this shouldn’t happen in a country as rich as this one.”

Despite solid economic growth, thanks in no small part to North Sea oil, and one of the lowest unemployment rates in Europe, voters also simply seemed to crave change, analysts said. “Norway is very rich,” said Frithjof Jacobsen, chief political commentator at the tabloid newspaper Verdens Gang, known as VG. “We have hardly any unemployment. So it must be strange to see the government changing from the outside. But eight years is a very long time.”

Mr. Stoltenberg has been prime minister since 2005. Last month, he sought to revive his chances of another term by driving a taxi in Oslo, the capital, to “hear what people really think.” The stunt was at least partly staged, as some of the passengers had been recruited in advance and told to wait in a certain spot for Mr. Stoltenberg.

But Marianne Kiaer, a 45-year-old teacher who said she supported Labor in the last two elections but switched to the Conservatives this time, appeared to speak for many when she said, “Maybe eight years with Labor is enough.”

In Stavanger, Norway’s oil capital, Kjell Gamlen, 54, said he voted for the Progress Party because “we need something altogether new in Norwegian politics.”

Shara Ali, 20, a student and refugee from Iraqi Kurdistan who arrived in Norway in 2002, blamed the growing influence of the Progress Party on mainstream politics for delays in getting her citizenship. “We are all contributing,” she said of immigrant population. “We are working and paying taxes.”

As some feared a harder line on immigration in a future coalition, some political observers said any impact of the Progress Party as a junior partner in a coalition would probably be minor. “The Progress Party cannot be compared to the Front National in France or the Danish People’s Party or German neo-Nazi groups,” said Frank Aarebrot, a professor of comparative politics at the University of Bergen and a prominent political commentator. “Its libertarian streak is as strong as its anti-immigrant streak. The current leader is much more concerned with privatizing hospitals and schools than with immigration.”