Cyprus finance ministers are planning to impose a weekly limit on cash withdrawals, the BBC has learned.
The country's draft capital controls include export limits on euros and a ban on cashing cheques, says Newsnight economics editor Paul Mason.
In addition, fixed-term deposits will have to be held until maturity.
Cyprus's finance minister earlier confirmed that depositors with more than 100,000 euros could see 40% of their funds converted into bank shares.
But Michalis Sarris also said that Cypriot depositors with less than 100,000 euros in their accounts "will not be hit".
"The exact percentage is not... yet decided but it is going to be significant," he told the BBC.
Bank of Cyprus chairman Andreas Artemis later handed in his resignation.
Media reports said his letter would be examined by the bank's board of directors when they convened in the afternoon.
His resignation suggests the country's financial establishment is still reeling, says the BBC's Europe correspondent Chris Morris, reporting from Nicosia.
In other Cyprus-related developments:
- The Department for Work and Pensions has said British pensions will not be paid into Cypriot bank accounts for the foreseeable future and has advised expats to open UK accounts
- Piraeus, Greece's third-biggest lender, said it has signed an agreement to acquire all of the deposits, loans and branches owned by the Greek subsidiaries of three Cypriot banks - Bank of Cyprus, Laiki, and the Hellenic Bank - for 524m euros (£445m)
- The head of the eurozone group of finance ministers, Jeroen Dijsselbloem, said there were no apparent signs of increased withdrawals of savings from peripheral to core countries in the region as a result of the Cyprus crisis.
The final size of the loss faced by investors will depend on how the government decides to protect pensions, Mr Sarris said.
He confirmed that all Cypriot banks will remain closed until Thursday and that capital controls will be placed on the size and the amount of money people will be allowed to withdraw once the banks have reopened.
These restrictions would "probably be a bit stricter" on the country's two largest banks, Bank of Cyprus and Laiki, and would remain in place until the banking system "stabilises", he said.
The exact details of this "two tier system" would be hammered out with the banks later on Tuesday, he said.
Mr Sarris is expecting "some bleeding, some outflow" of funds once the banks reopen, but believes that once EU bailout funds begin flowing "in a matter of weeks", confidence will return.
Although the economy would be badly hit by the economic crisis, Mr Sarris admitted, he maintained that it could benefit from "an energy boom", referring to the exploratory Aphrodite gas fields off the southern coast of the island.
"Yes, there will be a problem but we will overcome it in a relatively short period of time", he said. He also said his government had renegotiated more favourable loans terms with Russia.
The Cypriot authorities had said all but the biggest two banks would open on Tuesday.
Banks have not been open since 15 March. Their reopening had been expected after Cyprus agreed a deal with the International Monetary Fund (IMF) and the European Union (EU) that releases 10bn euros in support.
It was conditional on Cyprus itself raising 5.8bn euros, most of which looks likely to come from depositors with more than 100,000 euros (£85,000) in Bank of Cyprus and Laiki or Popular Bank.
Members of the European Central Bank (ECB) have been emphasising their view that Cyprus is an isolated case within the eurozone, and that the proposed rescue plan would not be applicable to other eurozone countries.
Speaking to reporters at a conference in Prague, Ewald Nowotny, member of the ECB's governing council, said: "Cyprus is a special case. It is no model for other instances" - a view earlier expressed by Benoit Coeure, ECB executive board member.
On Monday, Jeroen Dijsselbloem, head of the eurozone's finance ministers, had spooked the markets when he suggested Cyprus's bailout could serve as template for crises elsewhere - comments he later retracted.
Many analysts had been concerned that the Cyprus crisis would spread to the wider eurozone had the country been forced to give up the single currency.
There were fears that the country's possible exit from the euro would trigger a loss of confidence across the single currency bloc, and prompt investors to withdraw from other troubled economies, such as Greece.