Cyprus' second largest bank has stopped customers withdrawing more than 260 euros (£221) a day from cash machines, as MPs said they needed more time to reach a deal to save the country's economy.
Parliament had been due to vote on Thursday evening on a 'Plan B' to raise the 5.8bn euros (£4.9bn) Cyprus needs to contribute if it is to get the 10bn euros (£8.5bn) from eurozone partners and the IMF.
But MPs said they needed more time to study draft legislation setting up a "national solidarity fund" - which would nationalise pension funds, with bonds issued against future natural gas revenues - and imposing capital controls to prevent a run on the banks.
A third bill proposes a restructuring of the heavily indebted banking sector, including measures to prevent the Popular Bank, or Laiki, going bankrupt.
"This consolidation process will prevent the risk of bank failures and protect in their entirety all insured deposits up to the amount of 100,000 euros," central bank governor Panicos Demetriades said before parliament met.
"It also creates conditions for the recovery of the banking system and guarantees jobs."
Local media reported the restructuring of the Popular Bank could raise an estimated 2bn euros for the government.
Banks in Cyprus closed their doors last Friday and will stay shut until next Tuesday, but as rumours spread that the Popular Bank would never re-open customers rushed to cash machines to withdraw what they could.
"I've been to five ATMs, looking for the one with the smallest queue. The others had really long queues, at least 40 or 50 people," Peter Larkin, a Nicosia resident waiting in line with his five-year-old daughter, said.
"There's a lot of rumours that Laiki is going to go bankrupt and that (their ATMs) will stop giving out money."
The central bank said the Popular Bank would not be closed down and the lender itself said it was the high demand for cash that had forced them to reduce the amount customers could take out from 700 euros.
The bank's employees staged an angry protest outside parliament amid the uncertainty, at one point breaking through a police cordon around the building.
Sky's Ashish Joshi, reporting from outside parliament, said: "They are afraid about losing their jobs.
"The word has got out that the banks might be sacrificed in some shape or form for Cyprus to come up with its obligation."
The island's banking sector could face collapse if a new bailout bill is not agreed, following parliament's rejection of one containing a levy on all bank accounts in the country.
The European Central Bank (ECB) has said it will only guarantee assistance until Monday night without a new aid programme being in place.
But as the Cypriot MPs debated, eurozone finance ministers extended a lifeline, saying they were willing to work with Nicosia on new plans to make the bailout work.
"The Eurogroup stands ready to discuss with the Cypriot authorities a draft new proposal, which it expects the Cyprus authorities to present as rapidly as possible," Eurogroup chairman and Dutch finance minister Jeroen Dijsselbloem said.
The country's largest bank, the Bank of Cyprus, appealed for MPs to pass a bailout deal.
"The Cyprus economy is on the brink and in a fragile state. The next move may prove its salvation or destruction," the bank said in a statement.
Meanwhile, ratings agency Standard & Poor's cut the sovereign long-term foreign currency credit rating on Cyprus deeper into junk status, lowering it to CCC from CCC-plus.