The Panama Papers showed the premier's wife owned an offshore company with big claims on Iceland's banks, a undeclared conflict of interest for Gunnlaugsson, infuriating many who hurled eggs and bananas in street protests calling for him to step down.
The banks collapsed as the global financial crisis hit in 2008 and many Icelanders blame politicians for not reining in their debt-fueled binge and averting a deep recession.
The more than 11.5 million documents, leaked from the Panamanian law firm Mossack Fonseca, have caused public outrage over how the world's rich and powerful are able to stash their wealth and avoid taxes while many people suffer austerity and hardship.
Mossack Fonseca, which specializes in setting up offshore companies, denies any wrongdoing. On April 5, the Panamanian government sought to defend the country's reputation.