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Iceland's prime minister has sensationally resigned two days after he was caught up in the offshore tax scandal.

Sigmunder David Gunlaugsson is the first victim from the leaked Panama Papers which revealed the tax-avoidance arrangements of the rich and famous around the world.

The documents claimed he and his wife set up a company in the British Virgin Islands to hide millions of pounds with the help of Panama law firm Mossack Fonseca.

The revelations sparked fury across Iceland, with thousands gathering outside parliament to demand he stand down and opposition leaders presenting a motion of no-confidence against him.

Gunlaugsson, who denies any wrongdoing, initially refused to quit and asked President Olafur Ragnar Grimsson to dissolve government and call a snap election.

But just hours later, he left it to his deputy to announce his dramatic U-turn. 

The Progressive party's deputy leader and Agriculture Minister Sigurdur Ingi Johannsson told Icelandic broadcaster RUV: 'The prime minister told (his party's) parliamentary group meeting that he would step down as prime minister and I will take over.' 

Leaked financial documents allege that he and his wife set up a company in the British Virgin Islands with the help of a Panamanian law firm. 

He is accused of a conflict of interest for failing to disclose his involvement in the company, which held interests in failed Icelandic banks that his government was responsible for overseeing. 

Gunlaugsson has said earlier today that he may dissolve parliament and call new elections if he were to lose the support of his junior coalition partner following an uproar over his offshore holdings revealed in the Panama Papers.