German and European bank officials have said Cyprus can amend the terms of its €10bn (£8.5bn) bailout.
Among those terms are the plans for a one-off bank deposit levy, which has caused a plunge in stocks around the world and sparked new fears of economic crisis in Europe.
A parliamentary vote on the controversial terms has been postponed until tomorrow evening.
As public anger on the island grew, Russia's President Vladimir Putin joined strong criticism of the move. "Putin said such a decision, if taken, would be unjust, unprofessional and dangerous," a spokesman said in a meeting with economic advisers. Russian companies have an estimated £12.5bn in the country.
And Joerg Asmussen, a member of the European Central Bank's governing council, said the exact terms of the bailout were still down to the Cyprus government.
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 (£5bn) remains."
The mooted levy was supposed to provide that contribution. Under the plan, people with up to €100,000 (£87,000) in Cypriot bank accounts would pay a 6.75% levy, while those with more money would pay 9.9%.
At its midday briefing, the ECB made no official comment.
Steffen Seibert, a German government spokesman, said: "How the country makes its contribution, how it makes the payments, is up to the Cyprus government."
After trading at a five-year high of over 6500 in recent days, the FTSE 100 Index slumped this morning 100 points following the new President of Cyprus' attempt to gather parliamentary support for the bailout. Japan's Nikkei ended the session more than 2.5% lower, while Germany's DAX fell 1.2% to 7,944 and the CAC-40 in France was 1% lower at 7,945. In London, banks were among biggest fallers.
The levy was greeted with fury across Cyprus, with many expected to withdraw their savings from banks to avoid being hit by the tax.
Parliament had been due to vote on the bailout plan this afternoon, but according to Cypriot media, that vote has now been postponed. The postponement is believed to have come as the new President Nicos Anastasiades frantically tries to amend the plan to limit its impact on those with smaller savings.
If parliament eventually votes in favour of the plan, Cyprus will be eligible for a €10bn (£8.5bn) bailout from its partners in the eurozone and the IMF.
Though Cyprus accounts for only around 0.2% of the combined output of the 17 EU countries that use the euro, the tax on depositors has stoked fears of bank runs in other troubled economies.
Questions and answers
Question: Why does Cyprus need a bailout?
Answer: Before the financial crisis Cypriot banks grew rapidly, lending large amounts of money to borrowers in Greece – and buying significant chunks of Greek government debt. Two years ago the IMF estimated Cypriot banks' combined assets were more than seven times larger than Cyprus's entire GDP. When Greece went into freefall, Cyprus took a big hit.
Question: So why didn't the government just nationalise the banks, like Northern Rock?
Answer: Precisely for the reason above. Cyprus was affected by the economic slowdown like everybody else, and its government could not afford to buy them out.
Question: So why does the EU want to make Cypriot savers pay?
Answer: Bailouts always come with strings attached, be they tax rises, austerity – or in this case, a tax on savings. The deal would require anyone with more than €100,000 (approx £85,000) in savings to pay almost 10%, and anyone with less to pay 6.75%. This was agreed due to the huge amount of deposits in Cypriot banks being from overseas clients, in many cases from dubious Russians suspected of money-laundering. Unfortunately for ordinary Cypriots, they've been hit too.
Question: What happens if Cyprus votes against the deal?
Answer: It's not certain. Either the conditions are eased, or Cyprus defaults on its debts, leaves the euro and looks for other sources of finance – which, ironically in this case, may be Russia.