Sigmundur Gunnlaugsson, Iceland's prime minister, has become the first casualty of the so-called Panama Papers scandal after he offered to resign Tuesday, his press office told CNBC. "The prime minister's action reflects his wish to not stand in the way of the important issues that still remain on the government's agenda being finished in this term, issues like housing reform and the reform of the financial system that he will continue to fight for in the interest of the Icelandic people," said a statement from the prime minister's office.

His move follows leaked files that showed his wife owned an offshore firm with big claims on the country's collapsed banks.

"In recent weeks, the prime minister and his wife have provided detailed answers to questions about the assets of the PM's wife," the statement said. "They have never sought to hide these assets from Icelandic tax authorities ... No Parliamentary rules on disclosure have been broken."

The prime minister asked the Progressive party's vice chairman, the current minister of fisheries and agriculture Sigurdur Ingi Johansson, to take the office for an unspecified amount of time, the statement said. The prime minister's press office told CNBC that the offer to resign had not formally taken place. As Iceland's government is a coalition, other parties have to approve the move.

Earlier, Gunnlaugsson had asked the country's president to dissolve parliament in the face of a looming no-confidence vote and protests.

However, President Olafur Ragnar Grimsson said he had asked for talks with the main parties before making a decision. Dissolving parliament would almost certainly lead to a new election. "I was not ready to agree to that request (for dissolving parliament) until I had a discussions with the leaders of other parties on their stand," Grimsson told reporters.

"I do not think it is normal that the prime minister alone ... should be given the authority to dissolve the parliament without the majority of the parliament being satisfied with that decision."

Earlier on Tuesday, Gunnlaugsson said on his Facebook page: "I would dissolve parliament and call for new elections as soon as possible" if he lost support among his ruling coalition members. On Monday, the opposition filed a motion of no-confidence and thousands of Icelanders gathered in front of parliament, hurling eggs and bananas and demanding the departure of the leader of the centre-right coalition government, in power since 2013.