Iceland's president asked the leader of the Left-Green Movement, Katrin Jakobsdottir, on Thursday to form a new government, although it came second in Saturday's parliamentary election.
The mandate deals a blow to Prime Minister Bjarne Benediktsson of the Independence Party who called the snap election in September after less than a year in office as a scandal involving his father prompted a government ally to drop out of his ruling coalition.
The Nordic island of 340,000 people, one of the countries hit hardest by the 2008 financial crisis, has seen an economic rebound spurred by a tourism boom. But a string of political scandals has hurt trust in government in recent years.
The election result showed a Left-Green-led coalition was possible if they joined forces with the Social Democrats, the Progressive Party and the Pirate Party. Together, they would hold 32 of parliament's 63 seats.
Jakobsdottir has said she may try to form a broad-based government.
The Independence Party, which has dominated Icelandic politics for decades, fell short of a parliamentary majority.