It would also make them the biggest populist party in the Nordic region, topping the Danish People's Party, which gained 21 per cent in 2015, and would trump the 12.6 per cent for the far-right Alternative for Germany, which swept into the Bundestag previous year.
Mainstream politicians have so far ruled out co-operation with the Sweden Democrats. During this election, almost all of Sweden's major political parties-including the Social Democrats and the Moderates-agreed that Sweden should massively reduce migrant arrivals until a Europewide immigration and refugee policy could be reached.
Gains for the far-right are being blamed on voter fears of mass immigration. The strongest party, the Social Democrats, despite remaining first, still lost ground, standing at 28.4 percent (which is its worst result since 1908).
Kristersson's own Moderate party will have 70 seats in the new parliament, based on 19.8 percent of the votes.
"We will gain huge influence over what happens in Sweden during the coming weeks, months and years", he told supporters.
While the results need to be taken with caution - the votes of Swedish expats living overseas are not included yet and will only be released sometime this week, it seems clear already: the right-wing "populists" once again performed well, while finding a government will be tough for everyone involved.
Many online surveys, which in the last election had gauged the Sweden Democrats' vote better than conventional polls, had signalled they could dethrone the Social Democrats as the nation's biggest party - a position the centre-left has held for a century.
Susanne Madsen, 61, another Social Democrat voter, was confident Sweden's current prime minister, Stefan Löfven, would stay in place.
The Sweden Democrats, a party rooted in a neo-Nazi movement but which has been working to soften its image, has been breaking down longstanding taboos surrounding public discourse on immigration and integration. Parallel to that development, several opinion pieces of Swedish dailies have downplayed the racism of the Sweden Democrats.
Trump Demands Probe of Author Behind Anonymous Op-Ed
Ryan , said Thursday he is unaware of any role to that end that lawmakers could or should play. "I think it is national security. And, I would say, including the political people, because some political people knew about this as well".
Even with a third place, the Sweden Democrats is in a position to shake things up in the upcoming negotiations.
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.
"The alliance will not govern or discuss how to form a government with the Sweden Democrats", Kristersson said.
"It's not that they are shy voters, but that they are distrustful of the polling agencies", said Henrik Ekengren Oscarsson, a professor in political science at Gothenburg University.
The bloc led by Prime Minister Lofven's party won 40.6% of votes, or 144 seats, while the Moderates' bloc has 40% of votes, or 143 seats. He could try to build a similar government to 2014: a minority coalition with the Greens that relies on informal support in parliament from the ex-communist Left Party.
Responding to the call, Mr Lofven said he would continue to "calmly work" in his role over the next two weeks (when parliament opens), but acknowledged the election "should be the funeral for bloc politics". No other party will consider the anti-migrant hard-right group in any form of coalition. Clearest winners are parties with a distinct stance on migration - the Left Party with 7.9 per cent (+ 2.2), the Sweden Democrats with 17.60 per cent (+ 4.7) and the centre-right Centre with 8.6 per cent (+2.5). Other than that, little is known about the views of the party .
At the party's rally on Saturday, Akesson strongly criticised Lofven's government for "prioritising" the cause of immigrants over the needs of citizens.
That message has resonated with a growing number of people in recent years, as concerns rose over high-profile incidents of gang violence, an influx of refugees and regional economic inequality.
Far-right parties have gained strength in several European countries, including Germany and Italy.