Allied with the anti-establishment Pirate Party, the Social Democrats and the Bright Future party, the Left-Green had been in talks since Sunday in a bid to forge a governing coalition with the centre-right Reform Party.
"It is evident that not all the parties are convinced to continue these negotiations so I have decided to stop them and I don't think that there is ground to continue," Katrin Jakobsdottir, the leader of the Left-Green movement, the second largest party, told state broadcaster RUV yesterday.
It was not yet known what would happen next.
Asked if she would now return the power to form a government to the president, she replied: "I'm going to sleep on it."
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"The people want very much to see improvement in both the work in the parliament and the image of the parliament", Jonsdottir said at the time.
Since its independence in 1944, Iceland has only seen one centre-left government, which emerged from the 2009 election after the 2008 financial collapse.
The October 29 snap vote, prompted by a massive tax scandal ensnaring several Icelandic officials, saw the Pirates become the third largest party with 10 seats.
The Panama Papers, released in April, fuelled the resignation of former prime minister Sigmundur David Gunnlaugsson and prompted the snap vote.
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