Cyprus and its international creditors were in tense negotiations into the early hours Monday trying to hammer out a bailout deal that would preserve the country's place in the euro zone.

But political chaos in the island nation's capital fanned doubts about the government's ability to secure approval for any deal, putting the stability of the currency bloc in doubt.

Tensions nearly boiled over during meetings on Sunday evening, when Cypriot President Nicos Anastasiades threatened to resign amid demands from the International Monetary Fund and European officials for a deep restructuring of Cyprus's banking system, an official familiar with the incident said.

Cypriot officials and politicians have spent much of the past decade cultivating the country's status as an offshore tax haven, its banks swollen with deposits--mainly from Russia. With the rest of the euro zone now insisting that economic model can't continue, resistance from the Cypriot government and members of its parliament is running high.

Cyprus has kept Europe on tenterhooks over the past week, after its parliament rejected an initial EUR10 billion ($13 billion) bailout agreement it had reached with the euro zone and the International Monetary Fund. That agreement would have required Cyprus to impose a tax on depositors to raise EUR5.8 billion to help stabilize its two biggest banks.

Since then, communication between Europe and Nicosia has been strained. Officials in Brussels and other euro-zone capitals have complained about being left in the dark over the Cypriot government's plans and feared Nicosia's hunt for alternatives was wasting valuable time.

"Nobody seems in a position to call the shots," said a senior euro-zone official.

On Sunday night, officials from the IMF and the euro zone held parallel talks with Mr. Anastasiades, and the country's finance minister, Michalis Sarris.

But they didn't have much time. The European Central Bank has said it would cut off emergency liquidity to Cyprus's banking system on Monday night if there is no clear plan by then. That would prevent banks on the island from opening as planned on Tuesday and would quickly send Cyprus's financial system into free fall, potentially forcing the country to leave the euro zone. ECB officials insist the deadline can't be extended, because the central bank's rules prevent it from lending more to Cyprus's insolvent banks.

Even if the bailout goes through, the country faces a recession so deep that it may need even more money to survive inside the euro zone.

With its banks closed since March 16 and one or both of its two major lenders unlikely to survive the coming days, Cyprus--already more than a year in recession--is just beginning down the painful path being walked by Europe's crisis-ridden south.

Economists are fast dialing back their forecasts for the country's tiny, EUR17.5 billion economy, which until a few days ago was officially forecast to shrink 3.5% this year. Some now predict that the blow to Cyprus's financial sector, which accounts for about half of economic activity, combined with an existing credit squeeze made worse by the proposed bank-deposit levy, will send output into a tailspin.

"The [deposit] haircuts will have a calamitous impact on Cypriot output, leading to a decline in gross domestic product of 10% this year and 8% in 2014," said Gabriel Sterne at Exotix, a hedge-fund advisory. "We think the peak-to-trough decline in annual real GDP will be in the order of 23%, similar to Greece, but we see risks more on the downside than the upside."

As with the rest of Southern Europe, Cyprus faces crippling job losses, rising business bankruptcies and slumping tax collections, said economists.

That could imperil the country's ability to meet budget targets, something that in turn could call forth even harsher measures and once again stoke fears about the island's long-term future inside the euro zone.

Officials said they believe the financial and political gridlock has done long-term damage to the Cypriot economy. Restrictions on money transfers and possibly cash withdrawals now may need to be in place for weeks or months until Cypriot banks stabilize, officials said. And the government and its banks are likely to need more financing than they did a week ago because of the deteriorating economic climate.

"We are a week further and substantial damage has been inflicted on the Cypriot economy," said Dutch Deputy Finance Minister Frans Weekers as he arrived in Brussels. "So I wouldn't be surprised if [Cyprus's financial needs] will be more" than the amounts set out last week.

"The numbers haven't changed; if anything they have gotten worse," German Finance Minister Wolfgang Schauble said.

Amid the uncertainty over the island's financial future, the government has severely restricted the free flow of money to and from the island. Late Friday, the Cypriot parliament passed a bill that would allow it to shut the country's second-largest lender, Cyprus Popular Bank PCL (CPB.CP). The government was still fighting to keep its biggest bank, Bank of Cyprus PCL (BOCY.CP), alive.

Underlining the seriousness of the situation, the two banks imposed limits on cash withdrawals from automated-teller machines on Sunday. Georgios Georgiou, the spokesman for Cyprus's central bank, said the limit was EUR100 per day. However, at least one Bank of Cyprus ATM in Nicosia had a withdrawal limit of EUR120. ATMs of other banks in Cyprus dispensed cash normally, he said.

Cyprus's financial system is in trouble because of losses from Greek government bonds, inflicted during a euro-zone-led debt restructuring last year, and a quickly deflating real-estate bubble. The effects have been magnified by the large size of Cyprus's financial system relative to its economy.

Wealthy foreigners--many of them Russian--have used the island's lenders to store cash, taking advantage of lax banking laws and low corporate taxes. It was because of this reliance on deposits, which have reached about four times the size of Cyprus's economy, that the euro zone and the IMF insisted that bank-account holders contribute to the cost of saving the country and its banks.

In an initial deal reached March 16, the Cypriot government agreed to levy a tax of 6.75% on deposits with less than EUR100,000 and 9.9% on those above that amount--a one-time move that was supposed to raise EUR5.8 billion.

Since Cyprus's parliament voted down that deal, the government has failed to find other sources for that money. A trip to longtime ally Russia yielded no results and the euro zone rejected plans to nationalize Cyprus's pension funds and tap other domestic resources, arguing that would only further raise the country's debt load. But finance ministers, including Germany's Mr. Schauble, said they were ready to find a deal for Cyprus at Sunday's meeting.

"We are here to find a solution with Cyprus kept in the euro zone," said French Finance Minister Pierre Moscovici.

Whether a new deal will be able to keep Cyprus's debt-to-GDP ratio under 100% in 2020--the target that the IMF has set as a precondition for joining a bailout--is another question.

"Weaker GDP performance implies a higher debt-to-GDP burden," noted ratings firm Standard & Poor's. Last week, the firm cut Cyprus's sovereign-debt rating a notch to triple-C from triple-C-plus, saying it sees the economy now shrinking 6%, heightening the risk that Cyprus may not be able to meet the terms set for the loan.

"In light of building economic and financial-stability pressures, the terms of any support package are likely to be unpopular and challenging to implement in the context of a severe, protracted economic downturn and an extended bank holiday," the firm added.

--Tom Fairless and Maarten van Tartwijk in Brussels and Joe Parkinson and Matina Stevis in Nicosia, Cyprus, contributed to this article.

Write to Gabriele Steinhauser at gabriele.steinhauser@wsj.com, Matthew Dalton at Matthew.Dalton@dowjones.com and Alkman Granitsas at alkman.granitsas@dowjones.com

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