UPDATE 1-Euro zone commits to bail out Cyprus, but no details on how

* Euro zone to commit to Cyprus bailout by end-March

* No agreement yet on details of financing or whether "bail-in" necessary

* Cypriot finance minister concerned about depositor flight

BRUSSELS, March 4 (Reuters) - Euro zone finance ministers aim to reach a deal on bailing out Cyprus by the end of the month, but details of how the rescue will be financed will only be sorted out in the coming weeks, senior officials said on Monday.

Cyprus requested a bailout in June last year but it was not possible to reach an agreement with the last, communist-led government. A new, conservative government has now taken office and negotiations have intensified.

President Nicos Anastasiades promised on Thursday to work for a swift deal to prop up the island's banks, which need capital of around 8-10 billion euros. The total bailout, including financing for general government operations and to finance existing debt, could be up to 17 billion euros, equal to Cyprus's annual economic output.

Two euro zone officials said ministers meeting in Brussels had failed to agree on how best to finance the bailout, but were committed to agreeing on a rescue programme by the end of March, and would say as much in a statement.

"The (Eurogroup) statement will say that a deal is due at the end of March but there is no progress on what the programme should look like," one of the officials involved in the negotiations told Reuters, speaking on condition of anonymity.

The ministers examined a variety of options to finance the bailout and ensure that it is "sustainable" - that Cyprus can repay what it borrows.

Among the provisions expected is the privatisation of state assets, starting with the island's telecoms company which could raise up to 1.5 billion euros, and the restructuring of the bloated banking sector, which has assets eight times larger than the island's 17 billion euro economy.

German officials, backed by the Netherlands and Finland, have pushed for depositors in Cypriot banks, many of whom are Russian and British businesspeople, to help pay for the cost of the rescue, a process known as a "bail-in".

There are concerns in Berlin that Cyprus, with its low corporate tax rate and liquid banking system, has become a conduit for money laundering. Russian individuals and companies have a high level of deposits in the banking sector.

But Cyprus fears any "bail-in" will spark the rapid withdrawal of funds from the island and undermine its entire business model, making the economic situation even worse.

Figures released last week showed a little over 2 percent of total deposits was withdrawn in January, although officials say there has since been a return of capital.

Cyprus's newly appointed finance minister, Michael Sarris, called the bail-in idea a bad proposal.

"Really and categorically - and this doesn't only apply in the case of Cyprus but for the world over and the euro zone - there really couldn't be a more stupid idea," Sarris, a widely respected economist, told reporters last week.

He will push that line in discussions on Monday, the head of his office said, while adding that a variety of other options were open to discuss to make a bailout viable, including an extension of a 2.5 billion loan from Russia and the possibility of Russia taking a controlling stake in Cyprus Popular Bank, one of the hardest hit by the Greek debt crisis.

"SYSTEMICALLY IMPORTANT"

Olli Rehn, the European commissioner for economic affairs, warned over the weekend that the prospect of Cyprus leaving the euro zone remained a dangerous possibility, saying such a prospect should be a concern even for big EU economies.

"Even if you come from a big EU country, you should be aware that every member of the euro zone is systemically relevant," Rehn was quoted as saying in Der Spiegel in a veiled criticism of German Finance Minister Wolfgang Schaeuble, who has questioned whether the tiny island is systemically relevant.

"If Cyprus becomes disorderly insolvent, it is very likely that would lead to it exiting the euro zone," Rehn said.

While ministers will discuss Cyprus in detail on Monday, no decision is expected until later in March, when an extraordinary meeting will likely have to called to agree the rescue package.

Monday's meeting will also assess Ireland and Portugal, with the possibility that both countries will be given slightly longer to pay back the rescue loans they have already received.

While a small island economy, the difficulty with Cyprus is finding a way to make a bailout sustainable so that any money provided is repaid, especially given that public opinion in countries such as Germany, Finland and the Netherlands.

A 17 billion euro rescue would increase Cyprus's debts to around 145 percent of GDP, a level considered unsustainable. Greece's bailout calls for it to cut its debt-to-GDP ratio to 120 percent by 2020, but that would be too high for Cyprus.

The IMF and other officials believe Cyprus should have to cut its debt-to-GDP ratio to just below 100 percent, but Cyprus is likely to push back against that, saying 120 is manageable.