Speaking after the European Central Bank (ECB) said it was not increasing emergency funding to Greek banks, Mr Alexis Tsipras said Greek deposits were safe.
Greece is due to make a €1.6bn (AU $2.32bn) payment to the International Monetary Fund (IMF) on Tuesday – the same day that its current bailout expires.
Greece risks default and moving closer to a possible exit from the eurozone.
Greeks have been queuing to withdraw money from cash machines over the weekend, and the Bank of Greece said it was making “huge efforts” to keep the machines stocked.
Greek banks are expected to stay shut until 7 July, two days after Greece’s planned referendum on the terms it had been offered by international creditors for receiving fresh bailout money.
The Athens stock exchange will also be closed on Monday.
Greece’s capital controls
A maximum of €60 (AU$86,40) can be withdrawn from an account in one day. Overseas transfers of cash prohibited, except for vital, pre-approved commercial transactions.
Source: BBC