NICOSIA (AFP) - Cypriots faced new worries on Tuesday after a huge international bailout as the chairman of the island's biggest lender resigned and banks stayed closed for two more days.

Hundreds of students protested in front of the presidential palace amid growing public anger at the European Union and International Monetary Fund over the 10-billion-euro (S$16 billion) rescue package.

Bank of Cyprus chairman Andreas Artemis reportedly tendered his resignation due to concerns about the punishing terms of the bailout that saved the Mediterranean island from bankruptcy.

Finance Minister Michalis Sarris warned that so-called "haircuts" on large deposits at the Bank of Cyprus and Laiki, the island's second biggest bank which is being wound up, could be a greater than expected 40 per cent.

Despite the deal Cypriots endured an 11th day without access to banks after authorities ordered them to stay closed until Thursday, to prevent a run on deposits that could send the island into meltdown.

Dr Sarris said Cyprus was facing an "emergency" and an "unprecedented experience" but added that he thought the banks would be able to open on Thursday.

Financial controls imposed by the government to limit how much Cypriots can withdraw or transfer should be lifted in "a matter of weeks", Dr Sarris said, without specifying the conditions.

But his words failed to soothe the anger on the streets as around 1,500 students marched on the presidential palace in Nicosia chanting "Hands off Cyprus".

"We don't know what our future is, and we are angry that it will not stop at those measures," said one of the youths who only gave his name as Christos, 16.

President Nicos Anastasiades said on Monday on his return from Brussels, where he secured the bailout in a last-minute deal, that the deal was "painful" but necessary.

But reforms to the bloated Cypriot financial sector demanded by the EU and IMF got off to a rough start when Bank of Cyprus chairman Artemis tendered his resignation, the Cyprus News Agency reported.

The bank's board was set to consider his resignation later on Tuesday.

Local media said he quit because of the condition that the Bank of Cyprus would have to absorb Laiki's debts, the appointment of an administrator without informing the group's management and the sale of the bank's branches in Greece.

The bailout hits investors with deposits of over 100,000 euros at both Bank of Cyprus and Laiki, and calls for the effective wrapping up of Laiki, with the expected loss of thousands of jobs.

Fitch ratings agency on Tuesday downgraded Bank of Cyprus and Laiki to default category and placed the island's third biggest lender, Hellenic Bank, on negative watch.

Greek lender Piraeus Bank said on Tuesday that it had signed an agreement to acquire all of the Greek deposits, loans and branches owned by the subsidiaries of the same three Cypriot banks.

Greek stocks dropped by 4.58 per cent in midday trading but European markets mostly rose and the euro recovered from four-month lows against the dollar, while Asian markets were mixed.

Stocks had tumbled a day earlier following comments by the head of the Eurogroup, Dutch Finance Minister Jeroen Dijsselbloem, suggesting the Cyprus deal could form the basis for future bailouts.

The Dutchman later clarified that Cyprus was a "specific case" but European Central Bank executive board member Benoit Coeure said on Tuesday that Mr Dijsselbloem was "wrong" to make the comments.

The deal has angered the many Russian investors who have deposits in banks in Cyprus, whose status as something of a tax haven was unpopular with other eurozone members.

Ms Natalia, 39, a housewife and trained economist who is married to a Russian company executive and lives in the coastal town of Limassol, said the situation, especially the closure of the banks, was "absurd".

But she added: "Like many other Russians, I came here for the sea, the good weather and fresh air for my children. That is still here. If the (international) school doesn't close down, we will stay."

Cypriot authorities said the continued bank closure was needed for the "smooth functioning of the entire banking system".

Despite Cyprus accounting for just 0.2 per cent of the combined eurozone economy, the crisis on the island had threatened to reignite the single currency's woes after bailouts for four other nations.

Cyprus's strategic location, its two British military bases and tensions with the Turkish-occupied north of the island have added a further dimension to the crisis.