A top European official has said the Cyprus bailout, agreed in last-ditch negotiations over the weekend, should become the bloc's default approach for dealing with ailing lenders.

Jeroen Dijsselbloem, who chairs the Eurogroup gatherings of the 17 eurozone finance ministers, said in an interview today that banks' owners and investors must be held responsible "before looking at public money or any other instrument coming from the public side."

Dijsselbloem, who is also Dutch Finance minister, said the €10bn Cypriot rescue marked a watershed moment in how to deal with failing banks.

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He commented that European leaders should be committed to “pushing back the risks” of paying for bank bailouts from taxpayers.

"If there is a risk in a bank our first question should be 'OK, what are you in the bank going to do about that?'," he told Reuters and the Financial Times.

Mr Dijsselbloem's comments came ahead of an announcement by Cyprus' central bank that all the banks in the country except the two biggest will reopen for business on Tuesday, more than a week after they shut down to prevent a run.

Laiki and Bank of Cyprus will remain closed until Thursday, and a withdrawal limit from ATMs of 100 euros ($130) a day will also remain in place until then, the bank said.

Financial institutions in the country have been shut since March 16 as Cyprus and its international lenders struggled to agree on a plan to raise funds so the island could qualify for a bailout package.

The 11th hour bailout package agreed over the weekend was welcomed by Prime Minister David Cameron, and the United States.

Russia, however, responded furiously to the deal - condemning it as 'stealing'.

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The arrangement with the EU has brought Cyprus back from the brink but will see investors with more than €100,000 in the nation’s largest banks forfeit a large chunk of their deposits.

"In my view, the stealing of what has already been stolen continues," Prime Minister Dmitry Medvedev was quoted by news agencies as telling a meeting of government officials.

Despite this Russia also signalled it would backstop the European Union's bailout of Cyprus despite anger that the weekend rescue deal would impose heavy losses on uninsured depositors, many of them Russian.

President Vladimir Putin ordered his government to negotiate the restructuring of a bailout loan it granted to Cyprus in 2011 - having rejected Nicosia's request for easier terms during crisis talks last week.

Putin "considers it possible to support efforts ... aimed at overcoming the crisis in the economy and banking system of this island state," his spokesman Dmitry Peskov said.

Meanwhile British Prime Minister David Cameron said the economic situation in Cyprus should be a “reminder of a couple of important home truths” for the UK.

Durring a visit to Ipswich, the Prime Minister said he was glad that savers with less than £100,000 in their accounts would be spared the one-off levy and insisted the Government was doing everything it could to protect soldiers and staff on the island.

But turmoil in Cyprus highlighted a couple of home truths for Britain, he said in a question-and-answer session after a speech on immigration.

"It is good that an agreement has been reached overnight and I think that is welcome for people in Cyprus," Mr Cameron said.

"I think the first proposals of taxing people with bank accounts under £100,000 was a complete mistake and I am glad that has been avoided.

"I think, from Britain's point of view, the situation in Cyprus is a reminder of a couple of important home truths.

"The first is it was right not to join the euro, we are better off outside the euro. We can have our own economic policy, our own monetary policy and mend our fragile economy, which is badly in need of mending.

"But I think the second lesson is that 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.

"Those difficult steps the Government's taking, there is no alternative to that.

"I think people can see that when they switch on their televisions and see what is happening in other parts of Europe.

"Certainly, we are good friends of the people of Cyprus, we have many connections there, we have many British people living there and we also have the direct responsibility for the soldiers and MoD personnel, the Foreign Office personnel, and we have made very clear that they will be properly protected and we are doing everything we can on that front."