Cyprus is reportedly working on a last-minute proposal to soften the impact on smaller savers of a bank deposit levy imposed as part of an international bailout.
A parliamentary vote on the levy, which is central to the bailout, was postponed until tomorrow.
In a radical departure from previous aid packages, eurozone finance ministers want Cyprus savers to forfeit a portion of their deposits in return for a €10bn bailout.
Cyprus has been financially crippled by its exposure to neighbouring Greece.
The decision, announced on Saturday morning, stunned Cypriots and caused a run on cash points, most of which were depleted within hours. Electronic transfers were stopped.
The originally proposed levies on deposits are 9.9% for those exceeding €100,000 and 6.7% on anything below that.
The Cypriot government is discussing with lenders the possibility of changing the levy to 3% for deposits below €100,000, and to 12.5% for above that sum, a source close to the consultations told Reuters on condition of anonymity.
The source said the discussions had the "blessing" of a Troika of lenders from the European Commission, the International Monetary Fund and the European Central Bank.
In Brussels, a spokesman for Olli Rehn, the European Commissioner for Economic and Monetary Affairs, said discussions were still under way in Cyprus.
"If the Cypriot leaders agree on a more progressive scale for the one-off levy, in view of making it fairer for smaller savers and provided this would have the same financial impact, the Commission would be ready to recommend that the Eurogroup endorse such an agreement," the spokesman said.
The move to take a percentage of deposits, which could raise almost €6bn, must be ratified by parliament, where no party has a majority.
If it fails to do so, President Nicos Anastasiades has warned, Cyprus's two largest banks will collapse.
One bank, the Cyprus Popular Bank, could have its emergency liquidity assistance (ELA) funding from the European Central Bank cut by 21 March.
A default in Cyprus could unravel investor confidence in the eurozone, undoing the improvements fostered by the ECB's promise last year to do whatever it takes to shore up the currency union.
A meeting of parliament scheduled for today was postponed for a day to give more time for consultations and broker a deal, political sources said.
The levy was scheduled to come into force on Tuesday, after a bank holiday on Monday.
Mr Anastasiades, elected only three weeks ago, has said savers will be compensated by shares in banks guaranteed by future natural gas revenues.
Cyprus is expecting the results of an offshore appraisal drilling this year to confirm the island is sitting on vast amounts of natural gas worth billions.
In a televised address to the nation tonight, Mr Anastasiades said he had to accept the tax in return for international aid, or else the country would have faced bankruptcy.
"The solution we concluded upon is not what we wanted, but is the least painful under the circumstances," Mr Anastasiades said.