Iceland's opposition called on the prime minister and government to resign and planned a no confidence vote after a leak of documents stoked anger over his wife owning a tax haven-based company with large claims on the country's collapsed banks.
The allegations in the so-called Panama Papers that were released globally over the weekend surfaced in Iceland last month, but the renewed spotlight and a planned protest later will increase pressure on Prime Minister Sigmundur Gunnlaugsson.
Gunnlaugsson told privately held Channel 2 he did not plan to resign.
"The government has had good results. Progress has been strong and it is important that the government can finish their work," he said. "I will listen to the peoples' stand in the next elections."
He said in a blog post last month his wife's overseas assets were taxed in Iceland and added in a radio interview he had put the interest of the public before his own in dealing with the financial claims.
However, opponents and local media have alleged a conflict of interest, and said that Gunnlaugsson should have been open about the overseas assets and the company.
The center-right government coalition of Gunnlaugsson, in power since 2013, is involved in striking deals with claimants of the bankrupt banks.
A spokesman in the prime minister's office has said the claims of the firm owned by the prime minister's wife totaled more than 500 million Icelandic crowns ($4.1 million).
More than 8,000 people had signed up on Facebook for a demonstration in the capital Reykjavik scheduled later on Monday to demand a new election.
"What would be the most natural and the right thing to do is that (he) resign as prime minister," Birgitta Jonsdottir, the head of the Pirate Party, one of Iceland's biggest opposition parties, told Reuters.
"There is a great and strong demand for that in society and he has totally lost all his trust and believability."
The coalition holds 38 of 63 seats in parliament, meaning a no confidence motion that the opposition may bring this week is unlikely to pass.
But mounting public indignation could hurt Gunnlaugsson. Many Icelanders blame politicians for failing to control bankers and for years of austerity after Iceland's big banks failed in 2008, sending the economy into a dive.
An online petition for Gunnlaugsson's resignation had roughly 23,000 signatures on Monday. Iceland has a population of around 330,000.
"It is only logical new elections take place," Arni Pall Arnason, head of the opposition Social Democratic Alliance, had told Reuters on Friday.
The details about Iceland are part of a huge data leak about possible tax evasion around the globe, much of it released on Sunday by the International Consortium of Investigative Journalists and news organizations.