UPDATE 3-Cyprus tries to rework divisive bank tax
* Nicosia races to revise bank levy before parliament votes
* Looking to cut hit on small depositors to 3 percent or less
* Euro, European stocks fall but temper losses
* President says cash-strapped island had no choice
* Putin says deal unfair, sets bad precedent
NICOSIA, March 18 (Reuters) - Cypriot ministers rushed on Monday to revise a plan to seize money from bank deposits as part of an EU bailout, in an effort to ensure lawmakers supported it in a vote later in the day.
The weekend announcement that Cyprus would impose a tax on bank accounts as part of a 10 billion euro ($13 billion) bailout broke with previous practice that depositors' savings were sacrosanct and sent a shiver across the bloc, causing the euro to tumble and stock markets to dive.
Ahead of the vote in parliament, the government was working on a plan to soften the blow to smaller savers, by tilting more of the tax towards those with deposits greater than 100,000 euros ($130,700) - many of them Russians, eliciting an angry reaction from President Vladimir Putin.
The government says Cyprus has no choice but to accept the bailout with the levy on deposits, or go bankrupt.
A Cypriot government source told Reuters the introduction of a tax-free threshold for smaller bank deposits was under discussion but not yet agreed.
The euro zone has indicated that changes would be acceptable as long as the return of around six billion euros is maintained. If the Cypriot parliament votes the deal down, the euro zone would face a real risk of being dragged back into crisis.
"It is up to the government alone to decide if it wants to change the structure of the ... contribution (from) the banking sector," European Central Bank policymaker Joerg Asmussen, who was pivotal in the weekend negotiations, told reporters on the sidelines of a Berlin conference.
"The important thing is that the financial contribution of 5.8 billion euros remains," he said.
Residents on the island emptied cash machines to get their funds over the weekend. The move also unnerved depositors in the euro zone's weaker economies and investors fearing a precedent that could reignite market turmoil that the European Central Bank has calmed in recent months with its pledge to do whatever it takes to save the euro.
The euro fell before tempering losses. European stocks did similarly, dropping two percent before more than halving losses.
In the bond market - often the most reliable guide to euro zone stress - safe haven German Bund futures shot up while Italian equivalents dived, suggesting some concern that Cyprus could infect its larger neighbours.
"The crisis is back," one bond trader said.
Brussels has emphasised that the measure is a one-off for a country that accounts for just 0.2 percent of European output. The worst fear is that savers in other, larger European countries become nervous and start withdrawing funds, although there was no immediate sign of that on Monday.
U.S. economist Paul Krugman wrote in The New York Times: "It's as if the Europeans are holding up a neon sign, written in Greek and Italian, saying 'Time to stage a run on your banks!'"
Cyprus's banking sector dwarfs the size of its economy and its banks have been severely hurt by exposure to much larger neighbour Greece.
Its open economy has meant that its banks also attract cash from Russians. Moscow is considering extending an existing 2.5 billion euro loan to help bail the island out and said it had come to no decision.
Russian President Vladimir Putin criticised the bank levy as unfair and setting a dangerous precedent.
"While assessing the proposed additional levy on bank accounts in Cyprus, Putin said that such a decision, should it be made, would be unfair, unprofessional and dangerous," Kremlin spokesman Dmitry Peskov told reporters.
Approval in Cyprus' fractious 56-member parliament is far from a given: no party has an absolute majority and three parties say outright they will not back the tax. A vote initially planned for Sunday was rescheduled to give more time to build a consensus.
Faced with a growing public backlash, Cypriot finance ministry officials began discussions with lenders on Sunday to lessen the blow for smaller savers.
On Sunday, a source close to the consultations told Reuters authorities were hoping to cut the tax to 3.0 percent from 6.7 percent for deposits under 100,000 euros. The rate for deposits above that would then be jacked up to 12.5 percent from 9.9 percent.
Cypriot President Nicos Anastasiades, a conservative elected just three weeks ago, said in a TV address that the tax was an alternative to a disorderly bankruptcy. It was painful, but "will eventually stabilise the economy and lead it to recovery".
Savers who lost money would be compensated by shares in commercial banks, with equity returns guaranteed by future revenues expected from natural gas discoveries, Anastasiades said. But many legislators remain unconvinced.
"Essentially parliament is called to legalise a decision to rob depositors blind, against every written and unwritten law," said Yiannakis Omirou, speaker of parliament and head of EDEK, the small Socialist party. "We refuse to subscribe to this."