LONDON (CNNMoney) -- Cyprus' banks will remain shut until Thursday to give regulators time to guard against a run on deposits, the Ministry of Finance announced Monday.

Cyprus agreed early Monday to raise billions of euros from big depositors at the Bank of Cyprus and Popular Bank of Cyprus, and to shrink its banking sector dramatically, in return for a €10 billion European Union rescue package.

The tiny island had allowed its banking industry to grow to about seven times the size of the economy, based on total assets, attracting depositors and businesses with its low rate of tax. But the banks were brought crashing down by losses on Greek government debt, pushing the country to the brink of bankruptcy.

Cypriot President Nicos Anastasiades said in a statement Monday that the bailout package would avert "the collapse and the bankruptcy of the state," and that the banking system "will be stabilized."

"The danger for the bankruptcy of Cyprus is definitely left behind and the tragic consequences for the economy and the society are averted," Anastasiades said. "I don't even want to think what our day would be tomorrow without an agreement."

The original terms of the bailout, announced on March 16, included a levy on all Cypriot deposits including those of less than €100,000 insured under EU rules. That provision was thrown out by Cypriot lawmakers but not before long queues had formed at ATMs as people rushed to withdraw their savings.

Limits on withdrawals were introduced and the banks remained shut all last week after the European Central Bank said it would cut off emergency funding if Cyprus was unable to agree to a bailout with the EU and International Monetary Fund. Monday was a scheduled bank holiday in Cyprus.

The ECB said Monday it would continue to provide emergency liquidity assistance, given the agreement on "restoring the viability of the Cypriot financial system," but would continue to monitor the situation closely.

By clinching a bailout, Cyprus has at least temporarily avoided financial collapse and secured its place in the eurozone, but will pay a high price as one of its main service industries contracts rapidly and foreign investors seek a safer home for their cash.

Deposits of over €100,000 at Bank of Cyprus and Popular Bank will be frozen until they have been restructured. Popular Bank will be split up, its viable assets and insured deposits transferred to Bank of Cyprus, and its non-performing loans moved into a bad bank that will be wound down.

Big depositors at Popular Bank face complete wipe-out, along with shareholders and bondholders.

The losses facing big depositors as part of a deposit-equity conversion at Bank of Cyprus have yet to be determined but could be around 30%, a Cypriot government minister said Monday. Again, shareholders and bondholders will be tapped first.

The Cypriot parliament last week gave the government powers to implement temporary capital controls, which would restrict depositors from moving their money out of the country. It remains unclear exactly what sort of restrictions will be implemented, however.

Anastasiades said in his statement that on Tuesday, Cyprus' Central Bank "will implement ... certain restrictive measures with regard to financial transactions," though he did not provide specifics.

"It concerns a very temporary measure, which will gradually be relaxed," he said. "I want to assure you that we will do whatever possible so that we can return soon to full normalcy."

CNN Wires staff and CNNMoney's James O'Toole contributed reporting.