The euro zone took the unprecedented step of taking a bite out of depositors' accounts in Cypriot banks to help pay for its bailout of the island's financial system, a high-risk decision that could erode savers' confidence across the currency bloc and add to popular anger over its handling of the crisis.

The decision to raise ?5.8 billion ($7.6 billion) from taxes on depositors—including individuals with small amounts in their accounts—risks a political backlash for the newly elected center-right government on the Mediterranean island and a wider political fallout for the euro-zone leaders who are guiding the bloc's crisis strategy.

Asian shares and the euro fell sharply in early trading Monday as markets reacted to the bailout. Japan shares dropped 2.1%, Hong Kong fell 2.0% and Australia fell 1.4%. "The feeling is that the euro crisis could be back and that you could see full-on contagion," said Shane Oliver, head of investment strategy and chief economist at Amp Capital in Sydney. "But I suspect that we are going to hear reassurances from other countries."

A tax on depositors—6.75% on deposits up to ?100,000, and 9.9% above that level—was the only way out for the bloc's finance ministers after Germany, the euro zone's biggest economy, and the International Monetary Fund insisted that financial aid to Cyprus should be limited to ?10 billion.

With the money due to have been withdrawn electronically from bank accounts over the weekend, politicians in Nicosia were discussing how they might adjust the levy to make it appear fairer. Monday is a public holiday on the island, when banks are closed, but European officials said contingency plans were being put in place to calm any turmoil in the country's financial system when the banks eventually reopened.

Since the global financial crisis began in 2008, few European bank depositors have taken losses. Denmark forced some large depositors to do so in 2011, when two midsize lenders collapsed. Iceland also decided not to repay foreign depositors when it suffered a bank crisis in 2008—although the British and Dutch governments stepped in to make sure savers didn't incur losses. In 1992, Italy imposed a small tax on its depositors.

As the currency union's finance ministers, the IMF and the European Central Bank worked to contain the cost of the bailout, officials early Saturday morning crossed a red line they had avoided during the five-year financial crisis: making depositors pay for saving their banks.

To get there, the ECB threatened to send Cyprus's two biggest banks into liquidation, a move that would have sunk the island's financial system and, its president warned, could have led to its euro-zone exit.

European officials on Sunday emphasized that the levy was a one-time tax for Cyprus—based on the huge size of its banking system compared to the relatively puny size of the country's economy—and wouldn't be replicated elsewhere in the currency union. But the deal sends a signal to the rest of the euro zone that the bloc's richer nations are increasingly reluctant to transfer the costs of insolvent banks and governments onto the shoulders of their own taxpayers.

Over 10 hours of tense negotiations, euro-zone finance ministers hammered out the rescue for Cyprus, a nation of 800,000 people, an economy of less than ?18 billion, and an opaque banking system with some ?70 billion in deposits, many of them held by Russians and other foreigners.

But the final deal has triggered protests and cash withdrawals in Cyprus, where it imposes losses not only on rich Russians who took advantage of the island's lax bank rules, but also on ordinary Cypriot savers and companies.

"It was the worst time in my life. It reminds me of the invasion of the Turks in 1974," said a Cypriot official involved in the negotiations.

On Sunday, the government in Nicosia delayed the planned vote in Parliament to adopt the tax just three weeks after national elections because of questions over whether it could get a majority for the measures. That has raised doubts on whether banks can reopen as planned Tuesday.

This account of the negotiations in Brussels, the discussions that led to them and the expected fallout, is based on interviews with eight officials who participated in or were briefed on the talks.

Going into the meeting Friday afternoon, the challenge was big: An initial assessment of Cyprus's finances in January revealed a financial shortfall of around ?17.5 billion—?10 billion of that just for its two biggest banks: Laiki Bank and Bank of Cyprus PCL.

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A bailout of the banks would have driven the country's debt load above 140% of gross domestic product, prompting demands from Germany and the IMF that depositors in Cypriot banks take on part of the burden. Those calls had encouraged many depositors to pull their money from Cypriot banks, or split them into several bank accounts to avoid breaching the ?100,000 deposit-insurance limit under European Union law.

Amid fears of a bank run, Dutch Finance Minister Jeroen Dijsselbloem called an emergency meeting of his counterparts for Friday afternoon.

The timing would allow EU leaders, who held a planned summit in Brussels Thursday and Friday, to avoid the Cyprus conundrum. Crucially, however, Monday is a public holiday in Cyprus, which would give officials an extra day to implement decisions involving deposits.

Just after 5 p.m., finance ministers, IMF Managing Director Christine Lagarde, ECB executive board member Jörg Asmussen and the EU's economic-affairs commissioner, Olli Rehn, filed into a meeting room on the fifth floor of Brussels's Justus Lipsius, which houses the EU's ministerial meetings and summits. Cyprus's newly elected President Nicos Anastasiades stayed behind in the country's delegation room on the seventh floor, ready to approve or reject any potential deals.

Mr. Rehn was the first to make a specific proposal. To raise funds, Cyprus should impose a special levy on deposits, taxing accounts of less than ?100,000 at 3%, those up to ?500,000 at 5% and those above at 7%. Such a "solidarity levy "—the brainchild of Thomas Wieser, an Austrian who chairs technical discussion among euro-zone finance officials, and Mr. Asmussen— could avoid a straight "haircut" on deposits, which they feared could be too destabilizing for Cyprus and the rest of Europe. The tax would be applied to all Cypriot banks, not just the two in deep trouble.

But Ms. Lagarde had something else in mind. The IMF chief presented a much more radical plan, in which deposits above ?100,000 in Laiki and Bank of Cyprus would have been cut by between 30% and 40%. The owners of senior bonds in the two banks would also have faced losses—a step that was ultimately rejected. That plan would have limited the international bailout to ?10 billion and raise some ?7.5 billion from depositors.

It quickly garnered the support of German Finance Minister Wolfgang Schäuble, as well as the delegates of Finland, the Netherlands and Slovakia—all countries with strong, bailout-wary parliaments.

Cyprus Finance Minister Michalis Sarris said losses on savings—whether through a straight-out haircut or a tax— weren't acceptable to his government. But Mr. Schäuble , who wanted Nicosia to raise at least ?7.5 billion from depositors rejected his alternative proposals.

"We found the plan tough, but clean and quick," said one of the officials involved in the talks.

At around 10 p.m. Mr. Sarris went to brief Mr. Anastasiades, who approved a more limited levy: 3.5% on deposits below ?100,000 and 7% on bigger accounts. At that moment, Cypriot officials took an unprecedented step: They decided to freeze all electronic transactions from the island's banks to prevent a last-minute pullout in case the deal was leaked. But when Mr. Sarris returned to the fifth floor to presented that proposal, he found few takers. After another round of discussions, in which Mr. Schäuble demanded a tax of as much as 18%, Mr. Sarris was ready to accept a levy of 12.5% on deposits above ?100,000 and 7.5% for smaller deposits.

He went back up to brief the president and Mr. Anastasiades rejected the deal, threatening to leave. At that point, around 1 a.m. a small group—including Ms. Lagarde, Mr. Rehn, Mr. Sarris, Mr. Schäuble, France's Pierre Moscovici, Mr. Asmussen and Mr. Dijsselbloem broke off into a separate room. It was then—as other ministers snoozed or played on their iPads— that Mr. Asmussen told Mr. Anastasiades that without a deal, Cyprus's two big banks faced insolvency, since they would have no prospect of European funds to repair their battered capital buffers, said people who were present. In that case, the ECB would no longer be willing to fund the banks with central-bank emergency liquidity, Mr. Asmussen said, these people said. The implication: The island's biggest banks might be unable to reopen after Monday's bank holiday.

Mr. Asmussen backed up the warning by calling ECB President Mario Draghi and letting him know the central bank might have to deal with the collapse of Cyprus's banks.

The ultimatum carried echoes of the ECB's threat to cut off emergency liquidity for Irish banks in late 2010, which forced a reluctant Irish government to accept a euro-zone bailout.

Mr. Anastasiades gave in, but insisted that no deposit be taxed at more than 10%. In a final round of talks, Mr. Sarris hashed out a compromise with the ECB's Mr. Asmussen, the IMF's Ms. Lagarde, Eurogroup head Mr. Dijsselbloem and the Commission's Mr. Rehn.The levies were settled upon, but levels were under discussion Sunday night in Nicosia, with the likelihood the rate for smaller depositors would be cut and those for larger ones raised.

"It's not a pleasant outcome, especially of course for the people involved," Mr. Sarris said Saturday morning. "But we believe that it is something that compared with other possible outcomes is the least onerous."

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