Thousands of Icelanders rallied in Reykjavik on Saturday to demand immediate elections on a sixth consecutive day of anti-government protests over the "Panama Papers" revelations which have already toppled the prime minister.

The leak of millions of documents exposing the hidden offshore dealings of political figures and celebrities across the world triggered huge demonstrations in Rejkjavik this week.

Prime Minister Sigmundur David Gunnlaugsson became the first political casualty of the scandal as he was forced to cave in to protestors' demands for his resignation over revelations that he and his wife owned an offshore company in the British Virgin Islands and had placed millions of dollars of her inheritance there.

The issue is particularly sensitive in Iceland following the 2008 collapse of the nation's three main banks, which plunged the country into a deep recession and left thousands mired in debt.

After Gunnlaugsson's resignation, there was a government reshuffle with Sigurdur Ingi Johannsson, a serving minister, taking over as head of the centre-right coalition comprising the Progressive Party and its junior partner, the Independence Party.

Although he pledged to bring the elections forward by about six months, there has been no let up in the protests or calls for the entire coalition's ouster.

Up to 6,000 people protested outside parliament on Saturday, according to a police estimate -- a major gathering in a country with a population of just 320,000.

Johannsson, who held the fisheries and agriculture portfolio in Gunnlaugsson's government, is seen by critics as emblematic of the old guard that turned a blind eye to the reckless investments that brought about Iceland's financial meltdown.

- 'Not renewed its mandate' -

Prime Minister Sigurdur Ingi Johannsson speaks in the Althingi Parliament House, in Reykjavik, Iceland, on April 8, 2016 Halldor Kolbeins, AFP

According to a poll carried out by Reykjavik University on Thursday and Friday, just over half -- 51 percent -- of Icelanders want to see a general election held as early as May or June, while 26 percent agree with Johannsson's proposal to hold the ballot in the autumn.

Another 23 percent want elections to go ahead as scheduled in April 2017, the poll showed.

Johannsson himself only enjoys the support of 23 percent.

By choosing to leave Finance Minister Bjarni Benediktsson and Interior Minister Olof Nordal -- both named in the Panama Papers -- in their posts, the new PM fuelled the protesters' anger.

Protesters waved placards calling for the two ministers to quit at Saturday's demonstration.

"After the events of this week, one after the other, it is outrageous that we have a government not expressing... remorse, not saying anything about tax havens, not having a word of excuse," said protester Jorun Sigurvarsdottir, 61.

On Friday, the parliament rejected an opposition motion of no-confidence in the reshuffled government, which -- as expected -- was voted down by 38 votes to 25.

Since the Panama Papers story hit front pages around the world, thousands of Icelanders have taken to the streets in a historic show of force with Prime Minister Sigmundur David Gunnlaugsson, becoming the first political casualty of the revelations Halldor Kolbeins, AFP/File

Another motion, calling for the immediate dissolution of parliament was similarly defeated.

But its critics remain undeterred.

"Those of us in opposition are in complete agreement over the situation. And it seems that the people agree with us," said Steingrimur Sigfusson from the Left-Green Movement.

The government "cannot claim to inspire confidence because it has not renewed its mandate" through an election, said Helgi Hrafn Gunnarsson of the libertarian Pirate Party, which has surged in the polls since the crisis.

Formed in 2012 to campaign for more transparency in politics, Internet freedoms and copyright reform, the party is now credited with a massive 43 percent of voter support.

Its popularity stems from massive frustration over the political establishment's role in two major financial scandals, the country's 2008 banking crash and now the Panama Papers leaks.

Offshore banking is a politically charged subject in Iceland, a country still scarred by the excesses of the 2000s when senior bankers used shell companies in tax havens to conceal their dealings in risky financial products which ultimately led to the banking collapse.