Cyprus is working to agree capital controls to help prevent a run on savings when banks eventually re-open following the nation's bailout.
The closure of Cypriot banks was extended until Thursday amid a rush to restructure the two biggest lenders Bank of Cyprus (BoC) and Laiki, also known as the Popular Bank.
The boss of the BoC attempted to tender his resignation, along with four other board members, in protest at the bailout condition that it would have to absorb Laiki's debts.
However the BoC board rejected the resignation of chairman Andreas Artemis and the other directors, in the wake of the appointment of an administrator to downsize the island's biggest lender as a condition for an international bailout.
"The board of directors has not accepted the resignations," a statement carried by the state CNA news agency said.
"In accordance with the articles of association of the company, the resignations will only apply if not withdrawn within one week."
Meanwhile, Fitch said it had put Cyprus's credit rating on watch for a possible downgrade as the restructuring of its banking system would hurt the economy.
It currently rates Cyprus as 'B', only two notches above levels where the agency considers borrowers vulnerable to default.
The 10bn euro (£8.5bn) rescue was secured when politicians agreed to seize cash from bank depositors with more than 100,000 euros in their accounts.
It amounted to a hit of up to 40% on the money held by such people banking with BoC and Laiki, finance minister Michalis Sarris told BBC radio - cash that will be swapped for shares in the lenders.
The country's president had earlier assured his people the rescue package he struck with the EU and International Monetary Fund was in their best interests, despite the prospect of years of financial pain ahead .
Nicos Anastasiades agreed to close down Laiki as part of the demanded reforms of the Cypriot financial sector - brought to the brink of collapse by its investments in neighbouring Greece.
The capital controls being discussed, preventing people moving funds out of the country, could last for a number of weeks and may include weekly withdrawal limits.
Cash machine withdrawals remain restricted while the branch shutdown is said to be hammering businesses, which have been without access to their funds for more than a week.
European leaders said a chaotic national bankruptcy that might have forced Cyprus from the euro and upset Europe's economy had been averted by the rescue - though investors in other European banks were alarmed by the precedent of losses for depositors in Cyprus.
The raid on uninsured Laiki depositors is expected to raise 4.2bn euros of the 5.8bn the EU and IMF had told Cyprus to raise as a contribution to the bailout, according to Dutch finance minister Jeroen Dijsselbloem.
The politician, who heads the so-called Eurogroup of finance ministers, has faced a backlash after he spoke of the need for lenders to banks to accept the potential risks of their failure in future.
The comment - interpreted as support for the terms of the Cypriot bailout to become a template for any future eurozone bailouts - was widely criticised after it had a knock-on effect on world markets.
Greek finance minister Yannis Stournaras later insisted that a bailout deal agreed for Cyprus only applied to the island country, after markets started to speculate.
"This solution concerns Cyprus only and no other country, because Cyprus has a particular banking system," Mr Stournaras said, following a meeting with Greek President Carolos Papoulias.
Meanwhile Russia was angered that its depositors in Cypriot banks would suffer huge losses, President Vladimir Putin has ordered officials to restructure a loan Moscow granted to Cyprus in 2011.