Outgoing Prime Minister Ulf Kristersson, who resigned in the wake of his right-wing bloc's election loss, is now expected to be asked to take on the task.
Sweden's Social Democrat leader Magdalena Andersson said she had failed to form a government with the country's election-winning centre-left bloc.
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"I can conclude that there is currently no possibility for me to form a government," she told reporters on Monday, adding that she would inform the speaker of parliament that she was "returning the mandate entrusted to me."
Andreas Norlén, the speaker, announced that he would talk with party leaders on Wednesday as they work to find the most suitable candidate to attempt to form a government.
"I envision that after those deliberations, I will be able to return with new information on how the process will move forward," Norlén said.
Norlén, who was reelected as speaker on Monday, had given the task of trying to form a government to Andersson on 18 September.
Outgoing Prime Minister Ulf Kristersson, who resigned in the wake of the election loss, is now expected to be asked to make an attempt.
Andersson's centre-left alliance holds a three-seat majority in Sweden's 349-seat parliament. The bloc, which also includes the Left Party, the Centre Party, and the Green Party, won a total of 176 seats in the Riksdag. Kristersson's right-wing bloc won 173 seats. The Social Democrats finished the election as the largest single party, winning 99 seats.
Following the election, Kristersson called for "constructive openness" across parties in order to work towards forming a government.
"Discussions will need to be held with all parties to find ways around these impasses and create the conditions for a stable and capable government," he said.
He is now believed to be looking to win over the Centre Party, which was once a part of the right-wing bloc.
However, its leader, Elisabeth Thand Ringqvist, has pledged to uphold centrist policies and has refused to support a government that gives influence to parties on the edges of the political spectrum.
In Sweden, if the speaker fails four times at getting their proposal for a prime minister approved by the Riksdag, then a snap election must be held.