Cyprus President Nicos Anastasiades says he is battling against eurozone demands that all bank customers pay a one-off levy in return for a bailout.
Mr Anastasiades said he shared people's unhappiness with the terms, whereby all bank customers would pay a levy of 6.75% or 10% on their bank deposits.
The EU and IMF have demanded the levy in return for a 10bn-euro ($13bn; £8.6bn) bank bailout.
An emergency session of parliament has been postponed until Monday.
Mr Anastasiades said it was the worst crisis since Turkey invaded in 1974.
"I fully share the unhappiness caused by a difficult and painful decision," he said.
"That's why I continue to fight with the eurogroup to amend their decisions in the coming hours to limit the impact on small depositors."
The president said Cyprus had had to choose between stabilising its finances or the eventual collapse of its financial system and exit from the eurozone.
Under the bailout's terms, people in Cyprus with less than 100,000 euros in their accounts would have to pay a one-time tax of 6.75%. Those with sums over that threshold would pay 9.9% in tax.
Depositors will be compensated with the equivalent amount in shares in their banks, and Mr Anastasiades promised that those who kept deposits in Cypriot banks for the next two years would be given bonds linked to revenues from natural gas.
Cyprus announced the discovery of a field containing between 5 and 8 trillion cubic feet of natural gas under the Mediterranean Sea in 2011 but Turkey disputes its drilling rights.
It is believed that eurozone leaders, particularly in Germany, insisted on the levy because of the large amount of Russian capital kept in Cypriot banks, amid fears of money-laundering.
The speaker of the European Parliament, Germany's Martin Schulz, has called for the levy to be revised to protect small-scale bank customers.
It is now clear that negotiators of the bailout in Brussels drastically underestimated the reaction in Cyprus, says the BBC's Mark Lowen.
A tiny eurozone economy feels it is being blackmailed by the most powerful, and the growing resentment will do nothing to foster European solidarity, our correspondent adds.
"The solution we concluded is not what we wanted but is the least painful under the circumstances," President Anastasiades said on TV.
"I bear the political cost for this, in order to limit as much as possible the consequences for the economy and for our fellow Cypriots."
The vote in parliament has been postponed to Monday afternoon. If the deal is defeated, state media say banks could be closed on Tuesday so as to avoid mass withdrawals.
The Cypriot president's Democratic Rally party - which has 20 seats in the 56-member assembly - needs support from other factions to ratify the bailout.
A spokesman for one of its coalition partners, the Democratic Party, told BBC News they wanted assurances that the deal would resolve the problems facing Cyprus before voting in favour.
Opposition leader George Lillikas, an independent, said the president had "betrayed the people's vote".
The speaker of the European Parliament, Martin Schulz, argued in a newspaper interview that there should be an exemption from the levy for savers, for example, who had less than 25,000 euros in their accounts.
"The solution must be socially acceptable," Mr Schulz, who belongs to Germany's opposition Social Democrats, told Germany's Welt am Sonntag newspaper.
The German Chancellor, Angela Merkel, defended the levy, saying: "I think it's a good step which will certainly make it easier for us to approve the help for Cyprus."
As with past eurozone bailouts, the deal must be approved by the lower house of parliament in Germany, the EU's biggest economy.
If the levy goes ahead, it will affect many non-Cypriots with bank accounts, including UK expatriates.
However, depositors in the overseas arms of Cypriot banks will not be hit. Bank of Cyprus UK and Laiki Bank UK both confirmed on their websites that there would be no impact.
Chancellor George Osborne said the UK would compensate any government employees and military personnel whose bank accounts were affected.
The levy itself will not take effect until Tuesday, following a public holiday, but action is being taken to control electronic money transfers over the weekend.