Cypriot President Nicos Anastasiades has arrived in Brussels to attend a series of emergency meetings, in an eleventh-hour attempt to reach a bailout deal with the EU.
Under the deal, a one-off tax of 20 percent is to be imposed on deposits over €100,000 (£85,000) in Bank of Cyprus in exchange for shares in the bank, said a source close to the talks
A separate 4 percent tax will be imposed on deposits of more than €100,000 in other banks, the source said.
The measures must be approved by parliament, but enough MPs have already signalled they will back the proposals for them to pass.
A rejected tax would have taken 6.75 percent from small savers and 9.9percent from larger investors, but caused outrage among ordinary savers in Cyprus.
In separate developments, a €100 limit was imposed on cash withdrawals from the island's banks.
The EU's commissioner for economic affairs, Olli Rehn, said the island had only "hard choices left" and must agree terms on Sunday.
Cyprus must raise €5.8bn (£5bn) to qualify for a €10bn bailout and avoid bankruptcy.
Anastasiades arrived at EU headquarters in Brussels around lunchtime, ahead of a meeting this evening of the Eurogroup of finance ministers from the 17 eurozone countries.
The source said the rescue plans involve splitting the country's second largest bank, Laiki, into "good" and "bad" banks. Good assets would be merged with Bank of Cyprus, the island's largest lender, with the toxic assets remaining with Laiki.
Administrators will then be appointed to liquidate those assets. The bank will not be closed but will be hugely reduced in size.
If a deal on an alternative agreement fails, the European Central Bank has threatened to cut off funding to the banks, meaning they would collapse, pushing the country out of the eurozone.
"The negotiations are at a very delicate stage," said government spokesman Christos Stylianides. "The situation is very difficult and the time limits are very tight."
"It is essential that an agreement is reached by the Eurogroup on Sunday evening," said Rehn. "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."
Rehn said the immediate future would be "very difficult" for Cyprus, but that the EU stood ready to help.
There is concern on the island that a levy on large-scale foreign investors, many of them Russian, would damage Cyprus's financial sector.
Cypriot finance minister Michael Sarris was rebuffed by Russia this week after travelling to Moscow for talks to secure alternative means of funding. Russia said it would act only after the EU reached a deal with Cyprus.
The Cypriot parliament has already voted to impose capital controls to prevent a large-scale flight of funds from the island.
Banks in Cyprus have been closed since Monday 18 March, and many businesses are only taking cash payments.
In an election year in Germany, Chancellor Angela Merkel is keen to avoid being accused of using German taxpayers' money to pay off wealthy Russian account-holders, some of whom are suspected to be involved in criminal activity.
About half of the island's depositors are thought to be non-resident Russians. European authorities believe much of the cash held in Cypriot banks belongs to Russian money launderers.