The prime minister previously refused to step down, claiming his wife's overseas assets were taxed in Iceland and insisted there was no fiscal wrongdoing. (The Washington Post)

The Panama Papers — a massive leak of documents detailing the alleged secret offshore holdings of some of the world's elite — appear to be sparking political furor over the globe.

And the strongest aftershocks yet from this weekend's leak have been felt in Iceland, with the prime minister announcing his resignation just two days after the disclosures, which included allegations involving an offshore company linked to his wife.

On Tuesday, Sigmundur David Gunnlaugsson, one of a number of world leaders facing questions about their finances after the Panama Papers release, told his Progressive Party colleagues that he would resign from his position as prime minister, though he planned to stay on as party chairman, according to local media. Gunnlaugsson's decision came as a number of groups threatened a second evening of protests outside Parliament in Reykjavik.

Prime Minister Sigmundur David Gunnlaugsson speaks to Parliament in Reykjavik. (European Pressphoto Agency)

Earlier in the day, the Icelandic prime minister had said that he hoped to call new elections to appease the protesters. However, Iceland's elected head of state, President Olafur Ragnar Grimsson, refused the request, saying he needed to talk to other party leaders in Parliament first.

“It is important for us Icelanders, as a nation, to agree on a successful way out of this situation,” Grimsson said during an address on Icelandic television.

Certainly, the protests in Reykjavik on Monday suggest that many Icelanders want a change. Police officers told the Associated Press that it was the biggest protest crowd they had ever seen: 8,000 or so, they estimated. Other estimates are far higher, with organizers suggesting that as many as 22,000 could have been in attendance.

Either number is a large protest by any standard, but in Iceland, with a population of about 330,000, they represent a sizable chunk — perhaps even as much as 6.6 percent of the population, if the higher estimates are to be believed. For a crude comparison, a protest in the United States involving that percentage of the total population would have about 21 million participants. And many of the protesters in Iceland appear to be deeply angered by the latest revelations: One man even hurled tubs of yogurt at the Parliament building and smeared the dairy product on the face of a police officer on Monday, the Icelandic newspaper Morgunbladid reported.

Gunnlaugsson had been one of a number of world leaders named in the Panama Papers documents, which were obtained by the German newspaper Süddeutsche Zeitung and later shared with other international media outlets. The controversy stems from a company owned by Gunnlaugsson's wife that was based in the British Virgin Islands, a well-known tax haven. The company, Wintris, later made a large claim on Iceland's collapsed banks after the 2008 financial crash.

The new documents appear to show that Gunnlaugsson had set up the company with his now-wife in 2007 through the Panamanian law firm Mossack Fonseca but that he sold his half of the company for just $1 before a new law that would have forced him to declare his ownership came into effect. Gunnlaugsson faces criticism that his links to the company constituted a major conflict of interest — in 2015, his government negotiated a deal between Iceland's failed banks and claimants that may have allowed his wife to reclaim significant amounts of money.

Gunnlaugsson has denied wrongdoing, and no evidence of tax evasion by him and his wife has been discovered. He had initially resisted calls to resign, telling Icelandic television that there was "nothing new" in the Panama Papers and that he had already given a full account of his wife's business dealings. Gunnlaugsson also walked out of an interview with a Swedish television crew after being confronted about the accusations on Sunday.

Significant numbers of Icelanders don't buy his explanations. In a country deeply shaken by the 2008 financial crisis, accusations of economic misdeeds are viewed with little charity. Many Icelanders had their personal savings wiped out after the country's banking system collapsed and the local currency plummeted. In 2009, there were protests outside Parliament in Reykjavik, with police forced to use tear gas for the first time in half a century.

This public anger had, in fact, sparked Gunnlaugsson's political career. The son of a former member of Parliament, Gunnlaugsson was a journalist known for his nationalistic stances; he had helped lead a grass-roots group called InDefence that pushed for the country to reject plans to bail out international creditors of Iceland's failed banks. Two successive referendums on these bailouts were later rejected by voters, in large part thanks to InDefence's campaigns, and Gunnlaugsson, representing the Progressive Party, was elected prime minister in 2013.

The current government is a center-right coalition between the Progressives and the Independence Party. It holds 38 seats out of 63 in Parliament, a comfortable majority. However, it may not be stable enough to weather this storm. Discontent over its policies already had been brewing over the past year, with thousands gathering outside Parliament last year to protest inequality and alleged corruption. Given these new revelations, the coalition government's survival appears tenuous: Bjarni Benediktsson, finance minister and leader of the Independence Party, has refused to back the prime minister, telling Morgunbladid that the revelations were a "heavy blow" to the government.

A new election could well mean a big change for Iceland. In a poll conducted before the Panama Papers revelations, the anti-establishment Icelandic Pirate Party had been favored to get 36.1 percent of the vote if an election had been called at the start of April, more than the Independence and Progressive parties combined. Birgitta Jonsdottir, leader of the Pirates, called on Gunnlaugsson to resign. "He has totally lost all his trust and believability," Jonsdottir told Britain's Guardian newspaper.

For the second time in less than a decade, tiny Iceland is at the center of a global debate about the international financial system's failings. As one protester put it to a reporter from Morgunbladid, Gunnlaugsson has become the most "famous Icelandic person in history overnight for all the wrong reasons."

More on WorldViews:

China moves to sidestep Panama Papers story

The Panama Papers are super awkward for Beijing

Watch: What are the Panama Papers?