Earlier Monday, Gunnlaugsson said he had not consider resigning after German newspaper Sueddeutsche Zeitung linked him to an offshore company where he allegedly had undeclared interest.
Sueddeutsche Zeitung claimed that secret papers it had allegedly obtained from a Panamanian firm selling offshore companies showed how his wife used the shell company Wintris to invest millions of dollars. They allegedly bought the firm together in 2007 but Gunnlaugsson sold his share to his wife in 2009.
Mossack Fonseca, the Panamanian firm at the center of the claims, has refused to validate the information contained in the leaks and accused reporters of gaining unauthorized access to its proprietary documents. It warned that using unlawfully-obtained data was a crime that it would not hesitate to punish by legal means.