The remarks came after Moscow had rebuffed requests from Nicosia for assistance to save Cypriot banks in which Russians have billions at risk and at least one euro zone minister, Finland's Alexander Stubb, said an EU accord would be reached.
Averof Neophytou, deputy leader of the ruling Democratic Rally party, said Cypriot political leaders were close to a compromise that would let parliament reverse its rejection of a rescue package offered by euro zone partners a week ago under which holders of bank deposits would suffer losses.
Finance Minister Michael Sarris, returning empty-handed from Moscow, said a bank deposit levy was back "on the table".
Germany warned Cyprus it was "playing with fire", with the clock running down to a Monday deadline set by the European Central Bank when it will sever essential cash flows to Cypriot banks if no bailout program is agreed.
Neophytou said there was "cautious optimism that in the next few hours we may be able to reach an agreed platform" consistent with the framework originally agreed with the EU.
In Finland, an ally of Germany in disciplining their euro zone partners, European affairs minister Stubb told Reuters he was confident Cyprus would accept terms for an EU rescue: "Why am I optimistic? Because there are no other options," he said. "They'll find a solution, if not today then over the weekend."
Loss of the ECB lifeline would effectively cause the banking system to collapse and could force Cyprus to give up the euro.
The pace of the unfolding drama has stunned Cypriots, who barely a month ago elected conservative President Nicos Anastasiades on a mandate to secure a bailout but were outraged to hear last weekend that it would involve a tax on savings.
Lawmakers threw the bill out on Tuesday, calling it "bank robbery" - a stunning rejection of the kind of strict austerity signed up to by Portugal, Ireland, Greece, Spain and Italy over the last three years of Europe's debt crisis.
Euro zone leaders, led by Germany, have offered Cyprus 10 billion euros ($13 billion), but only on condition it raises 5.8 billion of its own.
In Nicosia, there were persistent rumors of a new levy proposal was in the works targeting only big depositors with over 100,000 euros in Cypriot banks, many of them foreigners including Russians who have been major contributors to the boom in Cypriot banks since the island adopted the euro in 2008.
With hundreds of demonstrators facing off with riot police outside parliament, lawmakers were preparing to debate bills to nationalize pension funds, pool state assets and split the island's second-largest lender, Cyprus Popular Bank, into good and bad assets in a desperate effort to placate exasperated European allies.
Taking a first step toward financial consolidation, Cyprus arranged on Friday for the takeover of big Greek units of its banks by a Greek competitor.
Shares in Piraeus Bank in Athens shot up 20 percent before officials confirmed Piraeus would take control of the Greek units of Bank of Cyprus and Popular Bank, the two biggest retail lenders, both badly burned by exposure to Greece's own financial troubles.
"EDGE OF AN ABYSS"
With banks in Cyprus closed until Tuesday, depositors, who have been besieging bank cash machines all week, lined up again on Friday to withdraw what they could.
"Our so-called friends and partners sold us out," said Marios Panayides, 65, a protester at the parliament. "They have completely abandoned us on the edge of an abyss."
Retailers, facing cash-on-delivery demands from suppliers, warned stocks were running low.
"At the moment, supplies will last another two or three days," said Adamos Hadijadamou, head of Cyprus's Association of Supermarkets. "We'll have a problem if this is not resolved by next week."
The Bank of Cyprus urged the government to go back and cut a deal with the EU under which larger deposits over 100,000 euros would be taxed. It was preferable, it said, to a collapse of the system and return to the pound which would wipe out assets.
"There must be no further delay," the bank said.
EU officials criticize Cyprus for insisting on taxing even small savers whose deposits up to 100,000 euros benefit from a state guarantee - a measure Cypriot leaders favored in order to limit the losses for bigger depositors, many of them Russian and seen as vital to the future viability of the Cypriot economy.
EU leaders, notably Germans who face an election in six months, have been reluctant to give up on the bank levy since it protects them from accusations of using European taxpayers money to bail out big Russian investors in Cyprus.
On Friday, Finnish Prime Minister Jyrki Katainen said it was up to the biggest bank depositors to share responsibility.
While a bank levy has raised concern over eroding confidence in banks in other, bigger euro zone states, notably Spain and Italy, the leaders of the euro zone have made clear they believe they can contain any damage, even if Cyprus is forced into a bankruptcy that would lead to it abandoning the euro.
Germany had rejected a proposal to nationalize pension funds and demanded Cyprus take an axe to its banks.
Chancellor Angela Merkel told lawmakers that while she wanted to keep Cyprus in the euro zone, the country must first recognize it had no future as an offshore financial centre for wealthy Russians and Britons, two parliamentarians told Reuters.
Her finance minister, Wolfgang Schaeuble, said that muted reactions to the crisis in financial markets showed the euro zone was able to contain the Cyprus problem.
The head of the Eurogroup of euro zone ministers, Dutchman Jeroen Dijsselbloem, said it was focused on keeping Cyprus in the currency union. Asked whether a Cypriot exit was inevitable, he did not rule it out, however:
"All kinds of scenarios are possible and the scenarios we're focusing on are to come to a joint solution in which Cyprus is saved but in which the banking sector continues in a smaller but healthier form."
(Additional reporting by Jan Strupczewski and Luke Baker in Brussels, Karolina Tagaris and Costas Pitas in Nicosia, Georgina Prodhan in Vienna, Lidia Kelly and Darya Korsunskaya in Moscow, Paul Carrel in Frankfurt and Gernot Heller in Berlin; Writing by Matt Robinson; Editing by Alastair Macdonald)