Cypriot President Nicos Anastasiades is locked in bailout talks with EU, European Central Bank and IMF leaders in Brussels.
The finance ministers must decide on Sunday whether or not to approve the bailout.
Cyprus needs to raise 5.8 billion euros to qualify for a 10 billion euro EU bailout and avoid bankruptcy.
A eurozone official said the Eurogroup meeting had been rescheduled for about 20:00 local time from 18:00 because talks with Cypriot officials ahead of those discussions had overrun.
In another development on Sunday, Bank of Cyprus – the island’s biggest lender – further limited cash machine withdrawals to 120 euros a day.
With queues growing outside cash machines across the island, the second biggest lender, Laiki (Popular) Bank, also lowered its daily limit to 100 euros, Cyprus News Agency reported. The bank’s previous limit had been 260 euros per day.
Banks have been closed since Monday and many businesses are only taking payment in cash.
In the run-up to the crunch talks in Brussels, the EU’s commissioner for economic affairs Olli Rehn said Cyprus had only “hard choices left” and must agree terms on Sunday.
According to a source close to the negotiations, the rescue plans – as they stand – involve splitting Laiki Bank into “good” and “bad” banks.
Good assets would be merged with Bank of Cyprus and the toxic assets will stay in Laiki. Administrators will then be appointed to liquidate those assets. The bank will not be closed but will be hugely reduced in size.
The source said a 20% levy would be imposed on deposits over 100,000 euros in Bank of Cyprus in exchange for shares in the bank.
A 4% levy would then be imposed on deposits of more than 100,000 euros in other banks. This would need to be approved by parliament but enough MPs have already given their backing to ensure it would pass.
The changes would cut Cyprus’s banking sector by between a third and a half.
Cyprus’ parliament rejected a bank levy on small and large deposits earlier this week, but a levy limited to large deposits is said to be back in consideration following pressure from Brussels and Berlin.
The levy that was rejected would have taken 6.75% from small savers and 9.9% from larger investors. It caused widespread anger among ordinary savers in Cyprus.
Cyprus needs the approval of the “troika” – the IMF, ECB and European Commission – in order to present a rescue plan to eurozone ministers.
If a deal on an alternative agreement fails, the ECB says it will cut off funds to the banks, meaning they would collapse, possibly pushing the country out of the eurozone.
“The negotiations are at a very delicate stage,” said Cypriot government spokesman Christos Stylianides.
“The situation is very difficult and the time limits are very tight.”
Olli Rehn said: “It is essential that an agreement is reached by the Eurogroup on Sunday evening. This agreement then needs to be swiftly implemented by Cyprus and its eurozone partners.”
“Unfortunately the events of recent days have led to a situation where there are no longer any optimal solutions available,” he added.
He said it was clear that the near future for Cyprus would be “very difficult” but that the EU stood ready to help.
There is concern on the island that a levy on large-scale foreign investors, many of whom are Russian, would damage its financial sector.
But leading Cypriot bankers have urged parliament to accept a levy, with small savers exempted.
Correspondents say Germany has pushed hard for a levy on investors who have benefited from high interest rates in recent years, rejecting a Cypriot plan to use money from pension funds.
Cypriot Finance Minister Michael Sarris recently travelled to Moscow in an unsuccessful attempt to get Russian help.
Banks in Cyprus have been closed since Monday and many businesses are only taking payment in cash.
On Saturday afternoon more than 1,000 bank employees marched to the Cypriot finance ministry, stopping briefly at the presidential palace.
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