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Panicos Demetriades's warning came as International Monetary Fund chief Christine Lagarde urged Cyprus to meet its commitments under the €10bn ($13bn) deal sealed with eurozone partners at the weekend.
The revised plan, drafted in response to an angry backlash at home and jitters that roiled global markets, sees a one-time levy being dropped on bank savings below €20 000 but retained at 6.75% on deposits of €20 000 to €100 000 and at 9.9% for amounts above €100 000.
Given the amendments to the bill, the tax which was originally to have applied to all bank deposits "will not yield the estimated €5.8bn agreed by the Eurogroup", Demetriades told parliament's finance committee.
"If we secure €5.5bn it will be considered in breach of the agreement and perhaps will not be accepted," he said, as cited by the Cyprus News Agency.
The bill was to be voted on later on Tuesday by parliament, whose stamp of approval is crucial for the bailout deal to go ahead.
President Nicos Anastasiades has called on all parties to back the bailout, warning that the island faces bankruptcy if it is rejected.
Fearing a run on accounts, Cyprus has shut its banks until at least Thursday, with the local stock exchange closed for the same period.
The planned levy on bank savings was agreed during the negotiations for the sovereign bailout deal for Cyprus.
Under the original accord, Cyprus agreed to impose a levy of 6.75% on bank accounts up to €100 000 and 9.9% for larger deposits. The move was aimed at raising €5.8bn for the government.
But faced with a public backlash that spooked global markets, eurozone finance ministers told Cyprus on Monday to take another look at the proposal.
Eurogroup President Jeroen Dijsselbloem of The Netherlands said ministers "continue to be of the view that small depositors should be treated differently from large depositors".
The Eurozone finance ministers said there would be re-negotiations to "introduce more progressivity in the one-off levy", in other words increasing the tax rate on bigger holdings to ensure the same €5.8bn return.
However, the Cypriot authorities, wary of seeing a flight of capital from the debt-hit Mediterranean island, opted to leave the maximum tax at 9.9%, according to an amended tax bill seen by AFP.
Lagarde, speaking in Frankfurt before the revised bill was made public, said the IMF was "extremely supportive of the Cypriot authorities' intentions to introduce more progressive rates" on taxing bank deposits.
She said it was now up to Cyprus to make good its commitments.
"It's time to deliver," Lagarde told a financial congress.
Adding to the pressure on the newly-elected Cyprus leaders, a German government spokesperson said on Tuesday that chancellor Angela Merkel had called Anastasiades to stress that his country should hold talks only with international creditors on its bailout deal.
"The chancellor once again emphasised that the negotiations are to be conducted only with the troika," the spokesperson told AFP, referring to the term used for the European Union, the European Central Bank and the International Monetary Fund.
The comment was made as the Cypriot Finance Minister Michalis Sarris headed to Moscow after an explosion of anger in Russia at the EU bailout deal for the island that could see Russian investors lose billions of euros.
Moscow, which has an outstanding €2.5bn loan to Cyprus and billions more in deposits in the island's banks, reacted angrily to the EU levy.
Russian President Vladimir Putin slammed the "dangerous" move and turmoil hit stock and currency trades on Monday amid concerns that a precedent had been set for bigger debt-saddled eurozone economies such as Italy and Spain.
Estimates vary but the Moody's rating firm estimates that Russian companies and banks keep up to $31bn in Cyprus, which accounts for between a third and half of all Cypriot deposits.
After markets suffered losses on Monday, Asian bourses rebounded on Tuesday as news spread that Cyprus was reworking the controversial savings levy.
Tokyo stocks led the way, closing 2.03% higher. However, Hong Kong suffered a late sell-off to end 0.19% lower.
The euro also rebounded in Asia, fetching $1 2961, up from $1 2957 in New York on Monday.
