Measures imposed last June at the height of Greece’s economic crisis limited bank withdrawals to 420 euros ($473) a week.
Athens was offered debt relief beginning in 2018 if that is necessary to meet agreed criteria on its payments burden.
Eurozone countries are expected to approve the loans, but Athens is unlikely to get debt relief because of the bloc’s differences with the International Monetary Fund.
Economic output shrank by 0.4 percent in the first quarter, and the country hopes to return to growth in the second half after years of recession.
Finance ministers from the 19-nation eurozone will meet Monday to find common ground between Athens and its international creditors.
Nearly 15,000 people protested tax hikes and pension cuts, which Greece will implement in exchange for another bailout.
Greek leaders on Saturday sought an explanation from the International Monetary Fund after a WikiLeaks release about the country's financial crisis.
The International Monetary Fund wants Greece to introduce additional spending cuts worth $2.75 billion before signing off on a third bailout.
"There was an agreement on all the milestones ... whatever was required," Greek Finance Minister Euclid Tsakalotos said early Tuesday. The deal would unlock $12.8 billion in aid to the cash-strapped nation.
Police fired tear gas at protesters throwing gasoline bombs Thursday during a nationwide strike following the acceptance of a third bailout.
The Greek state-owned bailout fund will supply at least $11 billion in aid to the country's four largest banks through purchase of convertible bonds and shares.
A new Greek parliament was sworn in on Saturday, and the debt-racked eurozone country faces immensely unpopular measures to free up more aid.
Alexis Tsipras, who led Greece through bitter bailout talks with the country's creditors, stepped down last month.
Political parties trying to form a new government have made no progress.
Greece is set to face its fifth national election in six years after Prime Minister Alexis Tsipras resigned Thursday, just after finalizing a bailout deal.
The move comes after Greece narrowly escaped an exit from the 19-member eurozone in July following months of uncertainty.
Greece repaid $3.7 billion to the ECB after receiving $14.5 billion from the European Stability Mechanism, the eurozone’s bailout fund.
The move will provide Greece sorely needed funds just ahead of a deadline to repay the European Central Bank.
The $1.37 billion deal, involving 14 regional airports, comes ahead of a German vote Wednesday on a third bailout package for Greece.
The Greek parliament on Friday approved a deal for a third bailout, but Prime Minister Tsipras faced scathing criticism from within his own party.