Greek businesses have been hit by limits on transferring money abroad to pay for imports of raw material and other items since capital controls started on June 29, and have had to apply to a special committee for permission to pay their foreign suppliers, a time-consuming process.
Stournaras said conditions for businesses were improving and authorities aimed to resolve pending issues in the next 10 days.
"As far as approvals are concerned, we are now very close to the monthly imports the Greek economy was registering before the crisis," he said after meeting business leaders on Friday.
Greece reopened its banks on Monday after it secured a 7.2 billion euro bridging loan to pay its debt obligations and enacted tough reforms demanded by its lenders to start negotiations on a third bailout.
The banks' three-weeks shutdown has cost Greek businesses 3 billion euros, said the head of Athens Chamber of Commerce and Industry Constantinos Michalos, with many firms warning of closures as a result of the capital curbs.
Greece has approved requests for money transfers totaling 1.585 billion euros from June 29 to July 23, much of it earmarked for energy imports, according to the Bank of Greece on Friday.