Athens has paid around 2 billion euros to the International Monetary Fund and is no longer in arrears.
The repayment, and another 4.2 billion to the European Central Bank, was made after the EU agreed last week to 7 billion euros of emergency funding assistance to Greece.
In the meantime, Greek banks reopened on Monday after being closed for three weeks.
The withdrawal limit has been capped at 420 euros per week.
Many Greeks complain about the limit, calling it an obstacle.
"But they did not make that clear in their announcement, they didn't say "don't go to the bank today, wait until Friday to get the full amount". We are once more withdrawing only 60 euros a day, or we will have to wait until Friday for the full amount. This is very tiring for everybody."
Also on Monday, the country's Value Added Tax went up, affecting prices on a wide range of consumer goods.
The tax went up 10 points, from 13- to-23 percent, causing worry in most households and businesses.
Mary Christou is a coffee shop manager.
"Our business has already been impacted by the crisis over the past years. Now with the new VAT rates there will be an even bigger impact because people will be paying more on other products and it will not be so easy for them, financially, to go out for a coffee or a drink."
The increase in value added tax is only one of the austerity measures the Greek government agreed to in order to secure the country's third bailout.
More measures including pension cuts and strict curbs on public spending are likely to be implemented later.
Greek prime minister Alexis Tsipras is eyeing a fresh start and swift talks on the bailout aimed at keeping Greece afloat.
The third bailout for Greece could take around four weeks to negotiate.
