Greek banks will remain shut beyond Monday "by probably two days", a finance ministry source said as authorities struggled to contain the economic damage from a two-week closure brought about by a cash shortage.

A new expiration date for the bank holiday would be announced later on Monday, the source told AFP.

Junior finance minister Dimitris Mardas had earlier met with the management of leading banks on the issue.

The banks have been closed since June 29, with withdrawals by Greeks limited to 60 euros ($66) after the government called a referendum on EU-IMF creditors' terms for an international bailout.

To the surprise of many Greeks, including members of the ruling Syriza party, an even harsher set of terms was accepted by the Greek government on Monday.

The ECB is currently keeping Greek banks -- and by extension the Greek economy -- afloat via its Emergency Liquidity Assistance (ELA) facility, but it has frozen total aid at 89 billion euros ($99 billion).

On Monday, the ECB decided to keep the ELA steady hours after eurozone leaders hammered out a three-year bailout package for Greece worth up to 86 billion euros ($96 billion), in return for tax hikes, pension reform and tough privatisation pledges.

The bank restrictions have badly disrupted the operation of the already weakened Greek economy, mostly limiting consumer purchases to food and fuel for the past two weeks.

But authorities have been careful not to disrupt the busy tourism season by sparing foreign card holders from withdrawal restrictions.

Greek Economy Minister Yiorgos Stathakis this weekend said banks would reopen in the event of a bailout deal, but capital controls would have to stay in place for months.

"If there is a deal, banks will reopen very soon, within the week as soon as the ECB (European Central Bank) provides ELA," Giorgos Stathakis told the BBC.

But, he added, "capital controls will take a few months to be totally removed."