But the governing Social Democrats, led by prime minister Stefan Löfven, while maintaining their record of finishing first in every election since 1917, were projected to plunge to less than 26%, their worst score for over a century, and the main centre-right opposition Moderate party also slid badly, to about 18%.
In Sweden, the speaker of parliament typically consults all party leaders after an election before tasking the one most likely to succeed at forming a government.
Prime Minister Stefan Lofven, who brought the Social Democrats to power in 2014, said he meant to remain in the job. The number was far lower than the asylum-seekers Germany accepted that year, but the highest per capita of any European nation.
"What we, the Sweden Democrats, are saying, and which is considered incredibly controversial in Sweden, is normal politics in the rest of Europe".
Ahead of the election, promising prospects for the Sweden Democrats had many Swedes anxious about an erosion of the humanitarian values that have always been a foundation of their country's identity.
At the party's rally on Saturday, he strongly criticised Mr Lofven's government for "prioritising" the cause of immigrants over the needs of citizens.
Swedish right and left neck-and-neck as anti-immigration party gains
"This government we have had now. they have prioritized, during these four years, asylum-seekers", Akesson said, giving an exhaustive list of things he says the government has failed to do for Swedish society because of migrants. Lofven accused some of his opponents of being prepared to work with the far-right party, which he vowed his party would not to.
New Democracy, founded by an aristocrat and a record producer, won almost 7 percent of the vote in 1991, on the promise of strict immigration policies, cheaper alcohol and free parking, only to crash out of parliament three years later.
Sweden, recognized for its open-door immigration policy, has always been a destination for refugees.
The Social Democrats have led a minority government with the Greens since 2014, with the informal support of the ex-communist Left Party to pass legislation.
"Terrible! I just wanna cry when I think about it", said Veronica Lundqvist, referring to the Sweden Democrats after she left a voting booth in central Stockholm.
The center-right Moderates have become especially tough on immigration, echoing numerous positions of the Sweden Democrats. About 6,300 candidates sought the four-year terms.
The Sweden Democrats are bidding to become the biggest populist party in the Nordic region, topping the Danish People's Party, which gained 21 percent in 2015, and trump the 12.6 percent for the far-right Alternative for Germany, which swept into the Bundestag a year ago.
The Social Democrats and its allies have tried to appease anti-migrant sentiment in the country by urging more integration programs and resources for refugees in marginalized communities, and to help them access education. "Everything is about us", Akesson said.
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The article added: "The erratic behaviour would be more concerning if it weren't for unsung heroes in and around the White House". Mr Dowd, who stepped down in January, resigned after holding a mock interview with Mr Trump as a practice session, the book says.