REUTERS/Stigtryggur Johannsson
The connection was revealed in the Panama Papers, a leak of 11.5 million documents from a Panamanian law firm, Mossack Fonseca, that appeared to show connections between world leaders, including Gunnlaugsson, and offshore shell companies.
The prime minister walked out of an interview Sunday when asked about he and his wife's relationship with the offshore company Wintris.
He was pressed specifically about reportedly selling a company in the British Virgin Islands to his wife for one dollar - the day before a law passed in Iceland that would have required him to make public his holdings.
Now, thousands of people in Iceland are furious, calling for Gunnlaugsson's resignation and a vote of no confidence from the country's parliament.
"I'm here to show the authorities my disrespect," one protester told Bloomberg. "It is unacceptable that the people that govern the country and enact laws can't seem to follow the rules of society they create themselves and want the public to follow."