Cypriot officials gave the first indications of the steep losses facing large deposit holders at the island’s two biggest lenders, as hundreds of angry bank workers staged a demonstration outside the central bank and demanded the resignation of its governor.

Cyprus’s central bank chief said Tuesday that large depositors at the island’s biggest lender, Bank of Cyprus Pcl, could lose as much as 40% on their deposits. In a television interview later, the finance minister said large uninsured deposit holders at the second-biggest, Cyprus Popular Bank Pcl, might only see one-fifth of their money returned and could wait several years before being paid back.

“We are in no position to give you the exact amount this moment,” Mr. Demetriades told reporters, referring to the amount that will be taken from large deposits at Bank of Cyprus, but he added “it’s about 40%.”

Based on estimates from government officials, the losses would affect some 19,000 deposit-holders at the Bank of Cyprus who, combined, hold some €8.01 billion ($10.30 billion) in uninsured deposits. Uninsured savers at Cyprus Popular Bank, who hold a combined €3.2 billion, will lose most of that.

“Realistically, very little will be returned,” Finance Minister Michalis Sarris said in the interview broadcast on state television. “The amount [returned], could be 20%. Certainly, for depositors above €100,000 it could be a very significant blow,” he said.