The bank shutdown since June 29 is estimated to have cost Greece's crisis-hit economy 3.0 billion euros (USD 3.3 billion) in market shortages and export disruption.
Capital controls including a block on key transfers to foreign banks and a ban on the opening of new accounts remain in force, although a daily cash withdrawal limit of 60 euros (USD 65) has been relaxed.
The government is meanwhile expected to make a 4.2 billion euro payment Today to the European Central Bank (ECB), made possible by a short-term "bridge" loan of 7.16 billion euros granted by the European Union on Friday.
The loan will also allow the debt-crippled Greek government to make payments to the International Monetary Fund (IMF) outstanding since June.
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Greece's radical left government last week agreed to tough reforms -- including tax hikes, an overhaul of the ailing pension system and privatisations it had previously opposed -- in exchange for a three-year bailout of up to 86 billion euros that it is hoped will stop it crashing out of the eurozone.
On the other hand, the tax on medicines, books and newspapers eased from 6.5 per cent to 6.0 per cent.
Katseli said some 40 billion euros have been withdrawn from Greek banks since December by customers anxious over the safety of their deposits, seriously damaging the banks' ability to function normally.
She urged Greeks to bring their savings back to the banks to support the crisis-hit financial system.
For the first time in months, technical teams representing the creditors -- the European Union, the ECB and the IMF -- are expected in Athens in the coming week to assess the state of the economy.