Gunnlaugsson had been under intense pressure to step down since leaked documents hacked from a Panamanian law firm revealed his links to an offshore company, triggering mass protests in the capital.
Senior political figures in the Nordic nation have been holding emergency talks amid fallout from the Panama Papers leaks.
Critics said the revelations surrounding the offshore company, which allegedly had holdings in Iceland`s collapsed banks, shattered public confidence in Gunnlaugsson`s leadership and could harm the country`s international reputation.
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