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Greece repaid the roughly 2 billion euros ($2.2 billion) it owed to the International Monetary (IMF) on Monday, the international body reported.

"I can confirm that Greece today repaid the totality of its arrears to the IMF, equivalent to SDR 1.6 billion (about EUR 2.0 billion). Greece is therefore no longer in arrears to the IMF," said Gerry Rice, director of communications at the IMF in a statement on Monday.

"As we have said, the Fund stands ready to continue assisting Greece in its efforts to return to financial stability and growth."

The confirmation came after Reuters cited finance ministry officials saying that Greece had begun to repay the total of 6.25 billion euros ($6.8 billion) it owed to both the European Central Bank (ECB) and the IMF.

The ECB confirmed that it, too, had been repaid.

However, experts are worried that the next round of bailout talks is skating over one vital subject: Debt relief.

According to Reuters, Athens on Monday began paying back 4.2 billion euros in principal and interest to the ECB and 2.05 billion euros in arrears it has owed the IMF since it stopped repaying its debts at the end of June.

It is also repaying a 500 million euro loan to the Greek central bank.

The country is paying its bills using a 7.16 billion euro bridging loan secured last week after it agreed to a series of harsh reforms. The measures, which have to be put into law, should result in the country receiving its third bailout.

Talks over the details of a third, 86-billion-euro ($93 billion) bailout for Greece are due to start in earnest on Monday after euro zone parliaments gave them the green light last week.

Greek banks upped their use of European Central Bank emergency funding in June, tapping 86.77 billion euros, up from 77.57 billion euros in May, Reuters reported on Monday.

Debt relief dominates

However one thorny topic is likely to dominate discussions: that of debt relief for Greece. Even the International Monetary Fund (IMF) has advocated such a move – but the fund's former deputy director told CNBC that it should make the first move.

"If the IMF is serious about debt relief then the right thing for the IMF to do is to write off its own debt – the debt that Greeks owes the IMF," Ashoka Mody told CNBC Monday. "The IMF has adopted the position that Greece needs debt relief, but somebody else should pay for that."

Mody's comments come at a time when the IMF has raised concerns over debt relief for Greece, with Managing Director Christine Lagarde advocating extending the maturities on Greek loans. The country is already battling soaring debt levels, and debt is expected to hit 180 percent of GDP this year, according to the European Commission.

In an interview with French radio on Friday, Lagarde said that a third bailout plan for Greece would "categorically" not succeed without debt restructuring.

Matthew Lloyd | Bloomberg | Getty Image

The issue of debt relief is a thorny subject, however, particularly for countries like Germany, which feel that debt forgiveness could set a precedent for other indebted members of the single currency region.

Read MoreGermany gives Greek bailout the green light

Despite this, there were some signs at the weekend that even Germany – Greece's largest euro zone lender -- could be succumbing to growing pressure over debt relief. On Sunday, Chancellor Angela Merkel said in an interview with German broadcaster ARD that discussions over changing the maturities of Greece's debt or reducing interest payments would be possible after the first successful review of the new bailout package.

Greece: Not so happy Monday!

She reiterated that a major debt haircut could not happen within a currency union, however.

Despite some apparent softening of Germany's stance towards debt relief, Volker Wieland, one of Merkel's economic advisers who are known as the "wise men," told CNBC on Monday that the chancellor's comments did not signal a change of tack by Germany.

"I think there can be debt relief in terms of postponing interest but that's a different message from a debt haircut which would involve taxpayers in Europe (losing money)," he told CNBC Europe's "Squawk Box" Monday.

'Trauma patient'

Mody was critical of lenders' demands on Greece -- a country he likened to being like a "trauma patient."

"The right thing to do is to have more debt relief and less austerity, but when that penny will drop and how it will drop is an open question. Ultimately, the route being pursued by the IMF, ECB and the Germans is bound to make everyone a loser," he said.

Read MoreGreece approves tough austerity: What next?

The Greek crisis appears to be nearing a resolution, with Greek banks open once again on Monday after three weeks of closures and talk turning to the finer points of an aid package which, it is hoped, will keep the country in the euro zone. But Mody warned that Greece was not out of danger.

"This program has again, like the last ones, been set up for failure. Greece is essentially like a trauma patient – it's going through a debt deflation cycle where the more debt you pay, the more indebted you become because your incomes fall but the debt burden does not fall as fast," he said.

Against the backdrop of such debt dynamics, Mody forecast that Greece's problems would re-emerge in six to nine months' time. "Then we'll begin to see numbers on Greek GDP growth…which will show that: 'Oops, this is not working.' But the 'oops' will be only from those that have constructed this program -- everyone else is predicting it now."

—By CNBC's Holly Ellyatt, with contribution from Katy Barnato