Cyprus can amend the terms of a bailout deal that has sparked huge public anger and led to heavy cash withdrawals, German and European bank officials say.
President Nicos Anastasiades has been meeting MPs to discuss the terms, with a crucial debate and vote in parliament postponed until Tuesday.
The 10bn-euro ($13bn; £8.6bn) bailout agreed with the EU and IMF demands that all bank customers pay a one-off levy.
Asian and European stock markets fell on Monday amid the uncertainty.
Meanwhile, Russian President Vladimir Putin on Monday called the proposed levy “unfair, unprofessional and dangerous”, his spokesman said. Russian banks and businesses have significant deposits in Cyprus.
‘Robbing depositors’
The debate and vote in Cyprus’ parliament has now been postponed until 18:00 local time (16:00 GMT) on Tuesday. It was initially to have been held on Sunday.
The president’s Democratic Rally has 20 seats in the 56-member assembly and needs other parties’ support to ratify the deal.
Joerg Asmussen, a member of the European Central Bank’s governing council, said there would be no objection to Cyprus altering the bailout terms.
He said: “It’s the Cyprus government’s adjustment programme. If Cyprus’ president wants to change something regarding the levy on bank deposits, that’s in his hands. He must just make sure that the financing is intact.
“The important thing is that the financial contribution of 5.8bn euros remains.”
He said that, as Cyprus’s banking structure was different from others in the eurozone, with fewer private bondholders, there had to be a tax on ordinary savers.
At its midday briefing, the ECB said that it would make no official comment.
German government spokesman Steffen Seibert echoed Mr Asmussen, saying: “How the country makes its contribution, how it makes the payments, is up to the Cyprus government.”
Protesters in Cyprus have held up banners blaming Germany for the controversial bailout deal.
However, German Finance Minister Wolfgang Schaeuble insisted he and the International Monetary Fund had been in favour of “respecting a deposit guarantee for accounts up to 100,000” euros.
He said it was the Cypriot government, the European Commission and the European Central Bank that had decided on the levy terms and that “they now must explain this to the Cypriot people”.
President Anastasiades has been holding talks with ministers and lawmakers at the parliament building in Nicosia, which has been cordoned off to prevent protests.
The BBC’s Mark Lowen, in Nicosia, says there are suggestions Mr Anastasiades is looking at lowering the cost to those with smaller savings.
Under the currently agreed terms, depositors with less than 100,000 euros in Cyprus accounts would have to pay a one-time tax of 6.75%. Those with sums over that threshold would pay 9.9%.
Our correspondent says the president may want to lower the former rate to 3%, while raising the levy on the larger depositors to 12.5%.
An EU source told Agence France-Presse there could be a three-way split on the level of levy, grouped into accounts holding less than 100,000 euros, between 100,000 and 500,000 and more than 500,000.
Another Cypriot source suggested that no levy were be payable on accounts under 20,000 euros, but there has been no official comment on the various options.
Mr Anastasiades insists that without the bailout Cyprus could face bankruptcy and a possible exit from the eurozone.
The banks are closed on Monday for a national holiday and could remain shut on Tuesday to avoid mass withdrawals.
Correspondents say the president faces a tough task getting the deal through parliament.
Speaker Yiannakis Omirou, of the EDEK party, said: “Parliament is called to legalise a decision to rob depositors blind, against every written and unwritten law. We refuse to subscribe to this.”
Although Cyprus accounts for just 0.2% of European output, there are fears that savers in other weak European economies could become nervous and spark runs on banks.
‘Confiscation’
Russia has strongly criticised the Cyprus bailout deal.
Presidential spokesman Dmitry Peskov said on Monday: “Assessing the possible decision of imposing additional tax by Cyprus on deposits, [President] Putin said that this decision, if taken, would be unfair, unprofessional and dangerous.”
Prime Minister Dmitry Medvedev said: “It looks simply like the confiscation of other people’s money.”
The Moody’s ratings agency estimates that, at the end of 2012, Russian banks had placed $12bn in Cypriot banks, with corporate deposits at $19bn.
So Russian corporate and individual investors could lose up to $2bn.
The Russian government also gave Cyprus a 2.5bn euro loan in 2011. Russian Finance Minister Anton Siluanov told the Interfax news agency on Monday that Moscow would consider extending the loan period and restructuring the repayments.