Lines of three dozen people or more were common on the island, especially at Cyprus Popular Bank PCL, also known as Laiki Bank, the country's second-largest bank and most-troubled lender.
The government proposed restructuring the bank and creating unprecedented restrictions on financial transactions as the European Central Bank threatened to cut off bailout funds if the country's banks aren't stabilized by Monday.
Cyprus has been promised $12.9 billion in aid from the eurozone if it can come up with $7.5 billion on its own.
Cyprus and the eurozone created panic Saturday when they agreed the $7.5 billion, or 5.8 billion euros, should come from a tax on all bank deposits. Cyprus' Parliament rejected the proposal amid furious opposition.
The tax idea was viewed as a breach of the principle that small depositors' money should be safe in banks.
Germany has said it would oppose any solution that included nationalizing pension funds from state-run companies in Cyprus, The New York Times reported Friday.
As alarmed Cypriot depositors flocked to cash machines to withdraw as much money as possible, they found themselves suddenly able to withdraw only up to 260 euros, or about $335, a day -- down from 800 euros, or about $1,033 -- after Laiki announced the scale-back.
All Cypriot banks have been closed all week to allow time for a bailout deal to be reached.
The proposals before Parliament, if they take effect, would let authorities restrict non-cash transactions, curtail check cashing, limit withdrawals and even convert checking accounts into fixed-term deposits when banks reopen.
Parliament was to debate the 61-page bill Friday morning, less than a day after President Nicos Anastasiades presented it.
The bill scraps the controversial tax on bank deposits. It also puts underperforming loans and questionable assets into a so-called bad bank and moves healthy assets to the Bank of Cyprus, the nation's largest financial institution.
It additionally limits the amount of cash people can take out the country.
Eurozone finance ministers issued a statement late Thursday saying they were "conditionally satisfied" with most of the new proposals. The statement said the so-called troika of lenders -- the International Monetary Fund, the European Central Bank and the European Commission -- would assess the final measure Friday after the Parliament vote.