The European Central Bank (ECB) has warned it will cut off emergency aid to Cyprus if a bailout plan is not in place by March 25.
In a statement issued on Thursday, the bank said Europe's assistance is contingent on the approval of a new package in the Cypriot parliament.
At a meeting in Nicosia, the capital, politicians again ruled out an unpopular tax on bank deposits and agreed to set up an investment fund as part of a "Plan B", after an earlier rescue deal was voted down.
"Following a proposal by [President Nicos Anastasiades], there was a consensus reached and a unanimous decision was taken for the setting up of an Investment Solidarity Fund," government spokesman Christos Stylianides said in a statement.
The ECB is keeping the Cypriot banks alive by allowing them to draw on emergency support through the local central bank.
Al Jazeera's Peter Sharp, reporting from Nicosia, said the statement reflects the frustration of the ECB.
"The central bank has just had enough," he said. "As far as they are concerned, this has been dragging on now and it's doing the eurozone no good at all."
Meanwhile, several hundred protesters, many of them bank employees, rallied outside parliament after rumours that the island's second-largest lender, Cyprus Popular Bank was to be wound up. The central bank governor denied the rumour.
Demonstrators chanted: "Keep your hands off Popular Bank" and "Hands off the bank," while several jostled with riot police, briefly breaking through a cordon, about 100 metres from the entrance to parliament.
Stylianides said the proposal for the proposed new fund was being processed by government lawyers, while Averof Neophytou, acting leader of the ruling Disy party, said that if it is ready, "certainly it will be before [parliament] this afternoon".
"I want to believe we will find a solution to avoid bankruptcy of this country and we will manage this," Neophytou said.
No details were released of how the fund would be constituted, but media had earlier reported it would comprise proceeds from the nationalisation of state and private provident funds and from bonds issued against future natural gas revenues.
The Phileleftheros newspaper said this would raise around $4.5bn of the $7.5bn that Cyprus is required to amass to secure a $13bn eurozone bailout. It was not immediately clear how the remaining funds would be raised.
Cyprus is seeking ways to secure funding for its banks after politicians on Tuesday overwhelmingly voted against a highly unpopular measure that would have slapped a one-time levy of up to 9.9 percent on bank deposits as a condition the EU-led loan.
With that now in doubt, Cyprus must find other ways to raise cash to repay its debts.
Thursday's revised plan was hastily drawn up after Finance Minister Michalis Sarris failed to make progress at talks in Moscow to secure aid, as a tough-bargaining Russia sought lucrative assets in exchange for more help.
Eurogroup head Jeroen Dijsselbloem said that the Cyprus debt crisis poses a "systemic risk" that threatens to ricochet right through the eurozone.