All Cypriot banks will remain closed until Thursday, the central bank now says, and temporary measures will be placed on transactions when they reopen despite an EU/IMF bailout deal.
Earlier, the authorities said all but the biggest two would open on Tuesday.
The central bank now says all will remain closed to ensure the whole banking system functions "smoothly".
The bailout deal will see larger depositors in the two biggest banks, Bank of Cyprus and Laiki, lose money.
President Nicos Anastasiades said "very temporary restrictions" would be put on capital flows, but gave no details.
Controls to prevent money leaving the country are already in place.
Certain limits on the size of cash withdrawals are expected to continue.
'30% losses'
The banks' reopening came after Cyprus agreed a deal with the International Monetary Fund (IMF) and the European Union (EU) that releases 10bn euros in support.
It was conditional on Cyprus itself raising 5.8bn euros, most of which look likely to come from depositors with more than 100,000 euros (£85,000) in Bank of Cyprus and Laiki, known as Popular Bank.
The banks shut a week ago after the country's first money-raising solution, which would have hit smaller deposit holders as well as larger holdings, was rejected.
Laiki will be shut down, and deposits under 100,000 euros, which are guaranteed by the state under EU law, will move into the Bank of Cyprus to create a "good bank".
Deposits above that insured amount will be frozen and used to pay Laiki's debts and recapitalise the Bank of Cyprus, with depositor losses eventually converted into shares.
Major depositors, many of whom are wealthy Russians, will not be able to access accounts exceeding the 100,000-euro limit until the restructuring of the banks is complete.
A government spokesman said the losses on uninsured depositors would be "under or around 30%".
'Specific case'
On Monday morning, hopes that the deal would solve the crisis lifted shares.
But later, stock markets were rocked after the head of the Eurogroup of eurozone finance ministers suggested that the deal for Cyprus model could form a template in any future bailout.
Jeroen Dijsselbloem, the Dutch finance minister who as head of the Eurogroup played a key role in the Cyprus negotiations, said the deal represented a new template for resolving future eurozone banking problems.
"If there is a risk in a bank our first question should be 'OK, what are you in the bank going to do about that?'," he told Reuters and the Financial Times.
He later added a clarification, saying that Cyprus was "a specific case with exceptional challenges".
Mr Dijsselbloem said the pattern for bank rescues should see shareholders take the first hit, then bondholders, who lend money through financial markets, and only then should depositors with large bank balances be tapped.
The Cyprus deal puts the burden for dealing with problem banks on their shareholders and creditors - in this particular case, customers with large bank balances - rather than the government and taxpayers, or bondholders, who lend through financial markets.
-BBC