Iceland’s prime minister is expected to face calls in parliament for a snap election after the Panama Papers revealed he is among several leading politicians around the world with links to secretive companies in offshore tax havens.

The financial affairs of Sigmundur Davíð Gunnlaugsson and his wife have come under scrutiny because of details revealed in documents from a Panamanian law firm that helps clients protect their wealth in secretive offshore tax regimes. The files from Mossack Fonseca form the biggest ever data leak to journalists.

Opposition leaders have this weekend been discussing a motion calling for a general election – in effect a confidence vote in the prime minister.

On Monday, Gunnlaugsson is expected to face allegations from opponents that he has hidden a major financial conflict of interest from voters ever since he was elected an MP seven years ago.

The former prime minister Jóhanna Sigurðardóttir said Gunnlaugsson would have to resign if he could not regain public trust quickly, calling on him to “give a straightforward account of all the facts of the matter”.

The former finance minister Steingrímur Sigfússon told the Guardian: “We can’t permit this. Iceland would simply look like a banana republic. No one is saying he used his position as prime minister to help this offshore company, but the fact is you shouldn’t leave yourself open to a conflict of interest. And nor should you keep it secret.”

Leaked papers show Gunnlaugsson co-owned a company called Wintris Inc, set up in 2007, on the Caribbean island of Tortola in the British Virgin Islands, to hold investments with his wealthy partner, later wife, Anna Sigurlaug Pálsdóttir.