With most ballots counted, the ruling center-left Social Democrats had 28 percent of the vote, trailed by the Moderates with 19 percent and the nationalist Sweden Democrats with nearly 18 percent.
At the party's rally on Saturday, Akesson strongly criticized Lofven's government for "prioritizing" the cause of immigrants over the needs of citizens.
The latest opinion poll suggests that Prime Minister Stefan Lofven's ruling Social Democrats will substantially lose seats but still emerge a victor with an estimated 24.9 percent of the votes.
With deadlock looming, it could take weeks to form a government.
The polls showed far-right, anti-immigration Sweden Democrats would get 19.1 percent of the votes.
Either some form of cooperation between the center-left and Alliance or an accommodation with the Sweden Democrats is likely to be necessary. "The democratic revolution in Europe is underway!"
Sabina Macri, voting in central Stockholm, said the current political situation has left her questioning her future in Sweden.
The Sweden Democrats, with roots in the neo-Nazi movement, has said the large number of asylum-seekers presents a threat to Swedish culture and claims they put a strain on the country's generous welfare state.
The nationalist Sweden Democrats were on track to get 17.8 percent.
Far-right parties have made spectacular gains throughout Europe in recent years as anxieties grow over national identity and the effects of globalization and immigration following armed conflict in the Middle East and North Africa.
Polling institutes have suggested support for the anti-immigration Sweden Democrats (SD) could tick in anywhere between 16 and 25 percent, giving it significant influence and making it impossible to predict the make-up of the next government.
If the preliminary results are confirmed, the Social Democrats' result would be its worst showing in a century.
"The election is between potential democracy and potential facism", he told AFP. It's more that we have had an integration issue for maybe 20 years.
That could prove fatal for the Alliance, with the Liberal and Center parties repeatedly ruling out a deal with the far-right.
Ahead of the election, Prime Minister Stefan Lofven had warned, "The haters are mobilizing in Sweden and are egging on people against people".
Lengthy negotiations will be needed to build a majority, or at least a minority that won't be toppled by the opposite side.
The traditionally two biggest parties, the Social Democrats and the conservative Moderates, were together predicted to win around 40 percent of votes, down by 10 percentage points from the last elections in 2014.
Separately, Swedish tabloid Expressen interviewed a representative of the right-wing Sweden Democrats. "It's time to take responsibility and talk to the Sweden Democrats", he said.
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.