After the country of 10 million took in a record 163,000 migrants in 2015, some Swedes have been rethinking its immigration policies.
With nearly all districts having reported, the ruling center-left Social Democrats and Greens and their Left Party parliamentary allies had 40.6 percent of the vote, while the opposition center-right Alliance was at 40.3 percent.
Akesson told supporters on Sunday that the projected 63 seats his party would clinch in the 349-seat parliament is a victory. "It's not just about what happened two years ago when we had a lot of refugees". But some 200,000 votes from Swedes who live overseas, which could tip the balance, were only to be counted Wednesday.
The results Sunday made it unlikely any single party would secure a majority of the 175 seats in the Riksdagen, Sweden's parliament.
"We have strengthened our role as kingmaker".
Sweden's Prime Minister Stefan Lofven, leader of the Social Democratic Party, prepares to vote in Stockholm.
If results hold, the Sweden Democrats, a nationalist party with Neo-Nazi roots, will become the third-largest party in parliament, handing the governing Social Democrats a stinging setback.
Other parties vowed they would not work with the far right to form a coalition government. "The democratic revolution in Europe is moving forward!"
Some of their campaign promises include leaving the European Union and putting a freeze on immigration.
"This government we have had now, they have prioritised, during these four years, asylum-seekers", Mr Akesson said, giving an exhaustive list of things he says the government has failed to do for Swedish society because of migrants.
The center-right Moderates have become especially tough on immigration, echoing numerous positions of the Sweden Democrats.
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 a year ago.
During a heated debate Friday evening of party leaders, Akesson caused a stir by blaming migrants for the difficulties they often have in finding employment and not adjusting to Sweden.
"This election is a referendum about our welfare", Prime Minister Stefan Lofven said.
Another, smaller poll by TV4 had the Sweden Democrats taking 16.3 percent.
"The election is between potential democracy and potential facism", he told AFP.
With both options unpalatable to the traditional players, forming a government could take weeks. None of Sweden's seven other parties will countenance any form of cooperation with the Sweden Democrats.
The opposition is intent on ousting Lofven, with some Moderates willing to go so far as to put an end to Sweden Demorats' pariah status and open negotiations with them.
That could prove fatal for the Alliance, with the Liberal and Center parties repeatedly ruling out a deal with the far-right.