Iceland’s Prime Minster has asked the country's President to call snap elections amid mounting anger over his links to offshore banking - and had his request refused.

Ólafur Ragnar Grímsson declined to dissolve Reykjavik's parliament, despite days of demonstrations demanding a new government, saying he would consult other party leaders first.

“I need to determine if there is support for dissolving (parliament) within the ruling coalition and others," he added.

"The Prime Minister could not confirm this for me, and therefore I am not prepared at this time to dissolve parliament."

Iceland: thousands protest, call for PM to resign over ‘Panama Papers’ leaks

Sigmundur Davíð Gunnlaugsson had pledged to break apart his ruling coalition if he lost the trust of his partners after being named in the Panama Papers – a huge cache of leaked files naming individuals linked with a law firm specialising in shell companies.

He denied any wrongdoing following the revelations and defied calls to resign as thousands of people protested outside the country’s parliament building.

But in a statement on Tuesday, Mr Gunnlaugsson said he would dissolve parliament and call elections “as soon as possible” if his coalition partners can no longer support him.

“I am proud of my work in politics and not afraid to put it to the verdict of the electorate, whether that’s now or later,” he added. “I am also proud of my wife and the integrity and self-sacrifice that she has always shown.”

People gather during a protest on Austurvollur Square in front of the Icelandic Parliament in Reykjavic, Iceland, calling for the resignation of prime minister Sigmundur Davíð Gunnlaugsson on 04 April, 2016, (EPA)

The Prime Minister said he had discussed the matter with the leader of the Independence Party, the senior coalition party to his Progressives.

He said he would “happily answer” for his deeds and decisions, in public and private, and hoped to continue pursuing the vision for Iceland that drove him to enter politics.

The Panama Papers revealed that Mr Gunnlaugsson and his wife bought an offshore company, Wintris Inc, in 2007 but the politician allegedly did not declare his interest when elected to the Icelandic Parliament two years later.

Opposition parties had called for a vote of no confidence later his week as anger mounted over Mr Gunnlaugsson’s financial dealings during Iceland’s devastating financial crisis.

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There is no evidence that the Prime Minister, who sold his shares in Wintris in 2009, his wife or the company were involved in any tax avoidance, evasion or dishonest financial gain.

He is one of dozens of leaders and former leaders around the world named in a huge leak of more than 11 million documents from Panamanian law firm Mossack Fonseca.

Iceland’s President cut short a visit to the US to attend to the “very serious situation” at home and has responsibility for forming coalitions and emergency governments as head of state.

If parliament is dissolved, all parties will have 45 days to prepare for elections.