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Cyprus' central bank said all banks in the country will remain closed until at least Wednesday.
The banks were due to reopen on Tuesday morning.
Cyprus will introduce capital restrictions to prevent an outflow of money when its banks reopen this week but the measures will be "very temporary," President Nicos Anastasiades said this evening.
"The central bank will implement capital controls on transactions," he said in a televised address to the nation.
"I want to assure you that this will be a very temporary measure that will gradually be relaxed."
Anastasiades said the bailout deal reached overnight in frantic talks with the island's partners in the eurozone was "painful" but the best under the circumstances.
The FTSE-100 index closed down 14.38 points (0.02%) at 6378.38 today.
The US Treasury Department has welcomed the 'bail-in' agreement Cyprus has reached with international lenders, saying the financial stability in the eurozone was important to the United States.
The US Treasury said the agreement was "critical" and that they were monitoring developments closely.
Banks in Cyprus are due to reopen tomorrow however two of the biggest banks on the island, Popular Bank and Bank of Cyprus, will stay closed until Thursday, March 28, a Cyprus Central Bank source told Reuters.
The proposed bailout tax on bank accounts in Cyprus amounts to "legalised theft" according to Yury Pyanykh, president of the Association of Russian Businessmen in Cyprus.
Mr Pyanykh told Russia's state news agency RIA Novosti the measure will be successfully challenged in court:
“This is legalized theft. It contradicts fundamental international agreements. If they approve this measure, I can only imagine the number of lawsuits that will be filed and won.”
David Cameron has said the Cypriot banking crisis serves as a "reminder" to the UK that there is "no alternative" to the Coalition's current economic policy.
"While it is very difficult, there isn't an alternative to getting on top of our deficit, to getting our public spending under control, to making our economy more prone to growth," the Prime Minister said when asked about the Cyprus bailout during a visit to Ipswich.
Mr Cameron said the dire situation in Cyprus also proved "we are better off outside the euro", adding: "We can have our own economic policy, our own monetary policy and mend our fragile economy, which is badly in need of mending."
The PM, though, said he welcomed the financial aid given to the island nation and was "glad" those with bank savings under €100,000 would not face a levy, adding: "We are good friends of the people of Cyprus".
Latest ITV News reports
Cyprus' rescue deal has sent shivers through southern Europe after a key eurozone figure said it would be a model for future bailouts.
The future is uncertain for the people who must live with the consequences of Cyprus' "painful" bailout deal.