Interpol has issued an international arrest warrant for former Icelandic bank chief Sigurdur Einarsson.
Einarsson, who ran the collapsed Kaupthing's bank, told prosecutors he is willing to return to assist the police with their enquiries on condition he is not arrested on arrival.
The bank's former co-chief executive Hreidar Mar Sigurdsson remains in police custody, following his arrest last week on suspicion of several offences including embezzlement, falsifying documents and stock and bond trading violations.
Iceland's special prosecutor is currently investigating in excess of 20 cases of potential criminal activity connected to Kaupthing and the country's other collapsed banks.
Kaupthing is also under investigation by the UK Serious Fraud Office and a special inquiry team in Iceland over the issuance of certain large loans to parties with a vested interest in the institution.
After Kaupthing's loan book was leaked last August, it revealed key shareholders and owners were the bank's main borrowers.
A special report by Iceland's parliament revealed Kaupthing secretly owned almost half of its own shares.
Meanwhile, Jón Ásgeir Jóhannesson, one of the main shareholders in another of Icelands three main banks, Glitnir, Kaupthing and Landsbanki, has been hit by a $2bn lawsuit that accuses him of "fraud" which contributed to the collapse of Glitnir Bank.
The lawsuit, filed by the winding-up board overseeing Glitnir's liquidation, also targets Price Waterhouse Coopers (PwC) accusing it of "facilitating" the alleged fraud.
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