Greek banks, which have remained shut since June 29, are due to re-open on Monday, after the European Central Bank (ECB) raised the level of emergency funding available.
"From Monday, the services offered will be widened. All the banks will be open," Deputy Finance Minister Dimitris Mardas told Greece's ERT television.
He said there might be a weekly limit on withdrawals, rather than a daily one, BBC reported on Friday.
"If someone doesn't want to take 60 Euros ($66) on Monday and wants to take it on Tuesday, for instance, they can withdraw 120 Euros or 180 Euros on Wednesday," he was quoted as saying.
"This is a proposal we are processing and we think it's technically possible."
The announcement from the ECB came after Greek parliamentarians passed tough reforms as part of a Eurozone bailout deal on Thursday.
