The European Central Bank says it has increased emergency funding to Greek banks by €900m (£627m) for one week.
ECB president Mario Draghi said the bank had offered more help through Emergency Liquidity Assistance (ELA) following a request from the Bank of Greece.
Mr Draghi said the ECB's total exposure to Greece was now €130bn.
Speaking at an ECB press conference in Frankfurt, he said that debt relief for Greece was "necessary".
"It's uncontroversial that debt relief is necessary and I think that nobody has ever disputed that," Mr Draghi said.
"The issue is what is the best form of debt relief within our framework, within our legal institutional framework. I think we should focus on this point in the coming weeks."
Mr Draghi said the ECB continued to act on the assumption that Greece was and would be a member of the euro area.
- European Commission president Jean-Claude Juncker said finance ministers agreed on a €7bn (£4.9bn) bridge loan for Greece
- The ECB increased the amount of liquidity available to Greece over the next week
- Mr Draghi said that Monday's bailout agreement was intended to ensure that Greece becomes a "thriving economy" in the region
- Reuters reports that Greek banks will reopen on Monday, after closing last month.
Rates on hold
Mr Draghi said the ECB was in a position to extend help under ELA after eurozone ministers agreed "bridge" financing for Greece to keep its finances afloat, and after Greek MPs passed reforms as part of the bailout deal.
He expressed confidence that Greece would repay its €3.5bn (£2.4bn) debt to the ECB when it comes due on 20 July.
Mr Draghi's comments came after the ECB held eurozone interest rates at their historic low of 0.05%.
The ECB also maintained its bond-buying programme at €60bn a month.
The massive bond-buying programme was launched in March to prevent the eurozone falling into deflation. It also aimed to weaken the euro to boost exports and encourage consumer spending.