Banks are set to re-open in Greece on 20 July after being closed for nearly three weeks.
The announcement comes after the European Central Bank (ECB) raised the emergency funding levels.
The €60 (£41) cash withdrawal limit per day is to remain, confirmed officials, reported BBC News.
Deputy Finance Minister Dimitris Mardas told ERT television that the daily withdrawal cap might be changed into a weekly limit.
"From Monday, the services offered will be widened. All the banks everywhere will be open. If someone doesn't want to take €60 on Monday and wants to take it on Tuesday, for instance, they can withdraw €120, or €180 on Wednesday," said Mardas.
"This is a proposal we are processing and we think it's technically possible."
The ECB raised the emergency funding for Greek banks on 16 July in a bid to help them reopen after Athens was granted a new three-year loan.
"Several positive things have happened that could justify us to increase the ELA we approved today. Incidentally I didn't say how much. We substantially accommodated the request put forward by the bank of Greece recalibrated over one week. The increase would be €900m over one week," ECB President Mario Draghi told reporters at a news conference.
"Things have changed. We had a series of news with the approval of the bridging financial package with the votes, the various votes in various parliaments – to begin with, in the Greek parliament – which have now restored the conditions a raise in the ELA."