* No agreement yet on details or whether "bail-in" necessary
* Cypriot finance minister concerned about depositor flight
* Troika will send mission to Cyprus on Tuesday - ECB's Asmussen
By Annika Breidthardt and Jan Strupczewski
BRUSSELS, March 4 (Reuters) - Euro zone finance ministers pledged on Monday to agree a bailout for Cyprus by the end of March, but details of how the rescue will be financed are yet to be sorted out.
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 took office last month and negotiations have intensified.
The troika of European Union, International Monetary Fund and the European Central Bank would send a mission of experts to Cyprus on Tuesday for a technical analysis of the country's financing needs and to get a better understanding of the new Cypriot government, ECB board member Joerg Asmussen said.
President Nicos Anastasiades promised on Thursday to work for a swift deal to prop up the island's banks, which need capital of 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 did not agree on how best to finance the bailout, but were committed to a deal by the end of March.
"The Eurogroup called on the international institutions and Cyprus to accelerate their work on the building blocks of a programme, and agreed to target political endorsement of the programme around the second half of March," the ministers said in a statement.
Removing one of the stumbling blocs for an agreement, the new Cypriot authorities had agreed to an independent review of how Cypriot banks are implementing anti-money-laundering laws, the euro zone statement said.
That is likely to appease Germany, which has raised concerns about money-laundering on the island.
The ministers examined a variety of options to finance the bailout and ensure that it is "sustainable" - that Cyprus can repay what it borrows.
One way to help that goal is privatisation of state assets, starting with the island's telecoms company, which could raise up to 1.5 billion euros. Cyprus also needs to restructure 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 business people, 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 was to push that line in discussions on Monday, the head of his office said before the meeting, adding that a variety of other options were open to discussion to make a bailout viable, including an extension of a 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.
But Jeroen Dijsselbloem, who chairs the meetings of the finance ministers, when asked if bank depositors were safe, avoided a direct answer.
He said the details of the bailout would have to be worked out together by the International Monetary Fund, the European Central Bank and the European Commission.
"All the ... elements will have to be decided as soon as the institutions come back with a solution which is cooperative in reaching a feasible and sustainable solution to Cyprus, so all the questions of the elements will then be answered," he said.
While short on detail, the euro zone statement at least ends a dispute over whether Cyprus is important enough for the euro zone to come to its rescue - a debate started by Germany, which had said the "systemic relevance" of Cyprus was unproven.
Olli Rehn, the European commissioner for economic affairs, said over the weekend all euro zone countries were important.
"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.
"If Cyprus becomes disorderly insolvent, it is very likely that would lead to it exiting the euro zone," Rehn said.
Cyprus is a small island economy, but it is important to find a way to make a bailout sustainable so that any money provided is repaid, because of hostile 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.
The final decision on Cyprus is likely to come at an extraordinary meeting of the ministers later in March.