Prime Minister Sigurdur Ingi Johannsson announced his resignation after his centrist Progressive Party -- which had been governing in a coalition with the conservative Independence Party -- suffered a drubbing in yesterday's vote.
Final figures from the election, called after Johannsson's predecessor was forced out over revelations in the Panama Papers of a hidden offshore account worth millions, pointed to a deadlocked outcome.
The Independence and Progressive parties together won 29 seats in the 63-member parliament or Althingi, down nine from the outgoing assembly.
Johannsson, an unpopular figure over his perceived closeness to business, said he will remain in office until a new government is formed in the volcanic island nation.
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President Gudni Johannesson is set to task Finance Minister Bjarni Benediktsson of the Independence Party, which won 21 seats, with trying to form a new government.
Pirate Party co-founder Birgitta Jonsdottir said she was "thrilled" after the movement created by anarchists, hackers and activists picked up 10 seats, more than tripling its representation.
The Left-Green Movement also picked up 10 seats, the Social Democrats three, and the centrist Bright Future Movement four.
The centrist Regeneration Party, which won seven seats, could determine the fate of coalition talks but negotiations with the Independence Party could be tough.
The two parties fell out over holding a referendum on resuming the nation's EU membership talks which were stalled by the incumbent government.
"We have not been negative towards other parties or how governments should be formed," Regeneration leader Benedikt Johannesson told AFP.
The episode revived the seething public anger that erupted during the 2008 financial crisis, which wrecked Iceland's banking industry and plunged the country into recession, prompting it to seek a humiliating IMF bailout.
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