A member of Iceland's parliament says she is "shocked" after leaked documents showed the country's prime minister and his wife owned a secretive offshore company that opponents say represented a major conflict of interest, and she believes he will be forced to resign.

Asta Helgadottir, who is a member of the North Atlantic nation's Pirate Party, was one of the roughly 8,000 protesters who gathered outside the Althing, Iceland’s parliament, in the capital of Reykjavik on Monday.

"We are basically protesting that our prime minister, our finance minister and our minister of interior have all been affiliated with offshore tax havens in the so-called Panama leaks," Helgadottir said in appearance on CTV News Channel.

"(It) is quite awkward for the Icelandic democracy to actually have a prime minister that is on the same scale as some of the greatest dictators of the world."

Prime Minister Sigmundur David Gunnlaugsson, Finance Minister Bjarni Benediktsson and Interior Minister Olof Nordal were named in the Panama Papers, which saw 11.5 million files from the database of world's fourth biggest offshore law firm, Mossack Fonseca, released to the public on the Sunday.

"This is quite a shock for everyone, especially to hear that were three ministers that were actually affiliated," said Helgadottir.

Others named in the documents include: the president of Argentina, the president of Ukraine, the father of British Prime Minister David Cameron, childhood friends of Vladimir Putin and the widow of former dictator of Guinea Ahmed Sekou Toure.

The documents alleged that Gunnlaugsson and his partner, Anna Sigurlaug Palsdottir, who is now his wife, set up a shell company in 2007 called Wintris Inc. in the British Virgin Islands with the help of Mossack Fonseca.

The company allegedly held nearly $4 million in bonds in the country's three major banks -- Landsbanki, Glitnir, and Kaupthing -- which collapsed during the 2008 global financial crash that crippled Iceland.

As a member of the country's centre-right Progressive Party, Gunnlaugsson campaigned against bailing out foreign creditors.

He became an MP on April 25, 2009. On Dec. 31 of that year he allegedly sold 50 per cent of Wintris to his wife for $1, a day before a new Icelandic law took effect that would have required him to declare the ownership of the company as a conflict of interest.

Gunnlaugsson began his four-year term as prime minister in 2013.

"We were quite shocked (and) everybody is quite angry, especially because of the rhetoric that we have to support the Icelandic economy, that we have to continue to have the Icelandic Krona," said Helgadottir.

"And then when the prime minister’s wife's savings can't be in Kronur, why should we? What's the difference between the prime minister and normal people."

The allegations have prompted calls for him to resign, as well as for a non-confidence vote in parliament.

Former Prime Minister Johanna Sigurdardottir and Birgitta Jonsdottir, the popular head of the Pirate Party, were among those to call for his resignation.

Gunnlaugsson told the Althing on Monday that he will not step down, even as thousands of angry protesters blew whistles, banged pots and pans, set off fireworks and stomped on barricades outside.

"I have not considered quitting because of this matter nor am I going to quit because of this matter," Sigmundur David Gunnlaugsson told parliament. "The government has had good results. Progress has been strong and it is important that the government can finish its work."

The Icelandic prime minister told parliament that he and his wife have paid all their taxes in full and denied owning a shell corporation.

Helgadottir said it is "difficult to say" if Gunnlaugsson will resign, but predicted he will eventually be forced to step down.

"It is quite likely that the pressure will be too much that he will actually have to resign," she said.

She added that all parliamentary and committee meetings Tuesday have been cancelled, something that hasn't been seen in the past three years.

"We are taking the situation very seriously," she said.

With files from The Associated Press