A new draft bill discussed in Parliament's finance committee proposed to spare all deposits below €20,000 ($25,900) from a levy. Those between €20,000 and €100,000 would still have a 6.75 percent charge imposed, and those above €100,000 would be hit for 9.9 percent, in line with the original plan put forward at the weekend.
A vote in favor of the bank account confiscation is needed if Cyprus is to get €10 billion in rescue loans from its euro partners and the International Monetary Fund. The seizure of deposits is meant to raise €5.8 billion, which is part of the country's rescue.
If the vote fails to get through Parliament, Cyprus faces potential bankruptcy and a possible from the euro, which could reignite concerns in financial markets over the future of the single currency.
Although Cyprus is the smallest eurozone country to be bailed out, its planned rescue has sent shockwaves through the single currency area as it was the first time European authorities have targeted people's bank accounts. Other bailed out countries such as Greece, Ireland and Portugal have raised funds through imposing new taxes.
Proponents of the Cypriot account levy argue that this way gets foreigners who have taken advantage of Cyprus's low-tax regime to share the cost of the bailout of the country's banks, which have been hit hard by their over-exposure to bad Greek debt.
About a third of all deposits in Cypriot banks are believed to be held by Russians. As lawmakers wrangled, Finance Minister Michalis Sarris was to fly to Moscow Tuesday afternoon to meet with his Russian counterpart.
Opponents point out that a blanket charge on people's bank accounts will hurt ordinary Cypriots more, and could shake the confidence of all in the country's banking sector. And by going after deposits, European policymakers have set a precedent that could be repeated in the future. The worry of bank runs across Europe lies at the heart of the concerns in markets at the moment.
In a sign of the scale of disagreement over the deposit charge, the country's central bank governor, Panicos Demetriades, recommended that no accounts below €100,000 be touched. That level represents the amount of savings that are supposed to be insured if a bank collapses.
"We believe that deposits up to €100,000 should not be levied," said Demetriades. "The credibility of and trust in the banking sector depends on this."
Banks have been shut until Thursday to prevent a bank run. Demetriades said he expects at least 10 percent of deposits to be withdrawn when the banks re-open.
"We expect outflows, but the European Central Bank has assured us that it will provide adequate liquidity to the banks because it will consider them viable," he said.
Demetriades stressed the importance of the bill being voted on and passing in Parliament.
"It's important for the future of the banking sector and the economy that this bill is passed," he said in the committee meeting.
Christine Lagarde, the head of the International Monetary Fund which is participating in Cyprus's bailout, said in Frankfurt that the IMF was "extremely supportive of the Cypriot authorities' intentions to introduce more progressive rates in the one-off tax."
Eurozone finance ministers held a telephone conference Monday night, and concluded that small depositors should not be hit as hard as others. They said the Cypriot authorities should stagger the deposit seizures more, but insisted that the overall take should stay the same.
Recently elected Cypriot President Nicos Anastasiades spoke with German Chancellor Angela Merkel by phone Monday night. Merkel made clear that negotiations on the aid package should be conducted only with the so-called "troika" of creditors, said a German government spokeswoman, who spoke on condition of anonymity in line with department rules.
Cypriot government spokesman Christos Stylianides said Anastasiades informed Merkel that "the possibility of reducing the requirements from self-raised funds is being explored."