0318 GMT September 23, 2018
The prime minister is usually the leader of the party with the most votes, but Sweden's fragmented political landscape after Sunday's vote makes it impossible to predict who will build the next government, a process likely to take weeks, AFP wrote.
As expected, neither Social Democratic Prime Minister Stefan Lofven's center-left bloc nor the center-right opposition garnered a majority.
The far-right Sweden Democrats, with roots in the neo-Nazi movement, solidified their position as third-biggest party, though they have yet to shake their pariah status.
Far-right parties have gained strength in elections in recent years in several European countries, including Germany and Italy. Far-right leaders in Austria, Italy and France hailed the strides made by the Sweden Democrats.
"However the dramatic bloc battle plays out, it looks like it will be difficult for Sweden to have a functioning government," paper of reference Dagens Nyheter predicted.
Lofven met Monday with his party leadership to map out his road ahead.
Parliamentary group leader Anders Ygeman said "it could take weeks, maybe even months" before Sweden had a government in place.
Lofven's bloc enjoys a razor-thin one-seat lead over the opposition Alliance.
The Social Democrats won 28.4 percent of votes, down 2.8 points from the 2014 elections, their worst score in a century.
"Nevertheless, voters made the Social Democrats Sweden's biggest party," Lofven said.
He has extended an invitation to the opposition in a bid to break the deadlock.
"We need a cross-bloc cooperation," he told party supporters on Sunday evening.
The four-party Alliance has however rejected his offer, urging him to step down and make way for them to form a government.
"This government has had its chance. It has to resign," Alliance opposition leader Ulf Kristersson told his conservative Moderate party supporters.
The Alliance was meeting Monday to hammer out a plan forward.
Lofven is seeking a new four-year mandate but he will have difficulty setting up a stable government. He, like all of the other parties, has ruled out any cooperation with the far-right.
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.
But it would then be under constant threat from the Sweden Democrats, out to topple it at the first opportunity.
They are ready to block any attempt to pass legislation, such as the autumn budget bill.
Lofven could also invite the Centre and Liberal parties to join him at the negotiating table.
With one major caveat: the Centre and Liberals are members of the Alliance, together with the Moderates and Christian Democrats.
Despite their differences, notably on immigration policy, the Alliance parties that ruled Sweden from 2006 to 2014 have agreed to try to form a government together.
But that is no easy task.
The Alliance would need the far-right's support to obtain a majority.
It would have to either make policy concessions in exchange for the Sweden Democrats' support or offer key positions on parliamentary committees that draft legislation.
The far-right wants to curb immigration and has called for Sweden to leave the EU.
The Sweden Democrats won 17.6 percent of votes — up almost five points from the previous election.
The party's leader Akesson told Swedish public radio on Monday he expected to wield major influence.