The ruling Progressive Party’s deputy leader, Sigurdur Ingi Johannsson, who holds the fisheries and agriculture portfolio, told reporters Gunnlaugsson was stepping down and that the party had proposed to their junior coalition partner, the Independence Party, that he become the new prime minister himself.
The two parties discussed the matter on Tuesday evening but no agreement was reached. Talks are expected to continue.
The leaked documents from a Panamanian law firm that specialises in setting up offshore companies have shone a light on the finances of politicians and public figures from around the world, causing public outrage over how the powerful are able to hide money and avoid tax.
Adding confusion to the political crisis, a statement emailed on Tuesday night by government spokesman Sigurdur Jonsson said Gunnlaugsson had suggested that Johannsson take over as prime minister “for an unspecified amount of time”.
“The prime minister has not resigned and will continue to serve as chairman of the Progressive Party,” it said.
An Iceland government spokesman has said the claims against Iceland’s collapsed banks held by the firm owned by the prime minister’s wife – in which he also temporarily held a stake – totalled more than 500 million Icelandic crowns ($4.1 million). Gunnlaugson has said his wife’s assets were taxed in Iceland.
His decision to step down came after thousands of Icelanders gathered in front of parliament on Monday, hurling eggs and bananas and demanding the departure of the leader of the centre-right coalition government, which has been in power since 2013.
Opposition politicians, pushing for fresh general elections, also filed a motion of no-confidence in Gunnlaugson and the government on Monday. The parliamentary vote could still take place this week and could trigger elections if the motion is carried.
“It is clear our demand for new elections still stands,” Left Green Party leader Katrín Jakobsdottir told Reuters.
But Finance Minister Bjarni Benediktsson, from the Independence party, the junior partner in the coalition government which has absolute majority in parliament, said he hoped the coalition would continue.
“We have agreed to start talks with the Progressive Party and to try to continue the co-operation we have had and which has until now been very fruitful for the Icelandic nation,” he told Reuters.
Any new election could see victory for the anti-establishment Pirate Party, according to polls the most popular political force in Iceland, which espouses grassroots democracy and transparency.
Gunnlaugsson’s opponents say he should have been open about the overseas assets and the company, and that he had a conflict of interest because the government is involved in striking deals with claimants against the bankrupt banks.
Iceland’s main commercial banks collapsed as the global financial crisis hit in 2008 and many Icelanders have blamed the North Atlantic island nation’s politicians for not reining in the banks’ debt-fuelled binge and averting a deep recession.