Iceland’s Prime Minister Sigmundur David Gunnlaugsson has resigned, his party says, making him the first major political casualty to emerge from the leak of the so-called Panama Papers.

Mr Gunnlaugsson was one of 12 current and former world leaders to have his alleged hidden financial dealings exposed in an unprecedented leak of more than 11 million documents from a powerful law firm based in Panama called Mossack Fonseca.

“The Prime Minister told [his party’s] parliamentary group meeting that he would step down as Prime Minister and I will take over,” the Progressive party’s deputy leader and Agriculture Minister Sigurdur Ingi Johannsson told a live broadcast.

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Mr Gunnlaugsson had earlier asked the president to dissolve Parliament and call for new elections if he did not receive the backing of politicians to remain in office, but the president refused, citing a need to meet with junior coalition members.

Refusing a request to dissolve Parliament was unprecedented in Iceland, political observers said, but Mr Gunnlaugsson resigned soon after.

Pressure had been mounting on Mr Gunnlaughsson, 41, to resign after leaked documents showed his wife owned an offshore company with big claims on Iceland’s collapsed banks.

On Monday, the opposition filed a motion of no-confidence in the Prime Minister and thousands of protesters gathered outside Parliament in a sign of growing anger about what the opposition said was the failure of Mr Gunnlaugsson to disclose a conflict of interest over his wife’s company.

More demonstrations had been scheduled for Tuesday.

Following the resignation announcement, Iceland’s opposition party maintained that they still wanted to hold a snap general election, according to party officials.

“It is clear our demand for new elections still stands,” Left Green Party leader Katrin Jakobsdottir said.

Mr Gunnlaugsson’s company, named Wintris Inc and acquired in 2007, was intended to manage his wife’s inheritance from her wealthy businessman father, according to the Panama Papers.

The Prime Minister sold his 50 per cent share to his wife for a symbolic sum of $US1 at the end of 2009.

But when he was elected to Parliament for the first time in April 2009, as a member of the centre-right Progressive Party, he neglected to mention his stake in his declaration of shareholdings.