Banks have been shut until Thursday to prevent a bank run. Demetriades said he expects at least 10 percent of deposits to be withdrawn when the banks re-open.
"We expect outflows, but the European Central Bank has assured us that it will provide adequate liquidity to the banks because it will consider them viable," he said.
Eurozone finance ministers held a telephone conference Monday night, and concluded that small depositors should not be hit as hard as others. They said the Cypriot authorities should stagger the deposit seizures more, but insisted that the overall take should stay the same.
The new Cypriot proposal, if approved, would raise less funds than the €5.8 demanded. It was unclear how the shortfall might be made up.
However, Cyprus President Nicos Anastasiades told German Chancellor Angela Merkel in a telephone conversation Monday night that "the possibility of reducing the requirements from self-raised funds is being explored," government spokesman Christos Stylianides said Tuesday.
The two leaders were expected to speak again on Tuesday, Stylianides said.
Cyprus's central bank governor noted that the ECB "believes we have to try to protect guaranteed deposits."
Demetriades stressed the importance of the bill being voted on and passing in Parliament.
"It's important for the future of the banking sector and the economy that this bill is passed," he said in the committee meeting, adding that "we believe that once trust is restored, deposits will return."
Christine Lagarde, the head of the International Monetary Fund which is participating in Cyprus's bailout, said in Frankfurt that the IMF was "extremely supportive of the Cypriot authorities' intentions to introduce more progressive rates in the one-off tax."