Just hours ahead of an expected vote in the country's 56-member Parliament on the seizure of a percentage of deposits, officials sought to limit the impact on small savers.
A new draft bill discussed in Parliament's finance committee proposed to spare all deposits below €20,000 ($25,900) from a charge.
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.
In a sign of the scale of disagreement over the deposit charge, the country's central bank governor 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.
Banks have been shut until Thursday to prevent a bank run.
Finance Minister Michalis Sarris is to fly to Moscow Tuesday afternoon to meet with his Russian counterpart. About a third of all deposits in Cypriot banks are believed to be held by Russians.
Christine Lagarde, managing director of the International Monetary Fund, said in a speech Tuesday in Frankfurt that the IMF was "extremely supportive of the Cypriot authorities' intentions to introduce more progressive rates in the one-off tax."