The chairman of the eurozone finance ministers has warned that the IMF may not release the next payment in Greece's bail-out package.
Luxembourg Prime Minister Jean-Claude Juncker said IMF rules may stop it paying because Greece cannot guarantee its solvency for the next 12 months.
His comments will put more pressure on Greece to reduce its deficit.
The Greek Prime Minister is holding talks with opposition parties on Friday to gain support for austerity measures.
George Papandreou's government began a programme of privatisations on Thursday, but Mr Juncker has said the privatisation plan needs to be more ambitious.
A 12bn euro ($17bn; £10bn) payment is due to be made to Greece on 29 June, 3.3bn euros of which should come from the IMF. It is the fifth tranche of the 110bn euro loan package from the EU and IMF.
Mr Juncker said the IMF was assuming that if it decided not to make the payment the EU would step in and make it instead, although he said that countries such as Germany, Finland and the Netherlands may oppose that.
Under the terms of the bail-out, Greece was supposed to go to the financial markets to borrow 24bn euros in 2012.
However, as Greece has missed its deficit reduction targets, the chances of it being able to borrow money commercially next year are very small.
The IMF would like the EU to agree to make up the shortfall if necessary through a second bail-out package, but that could be unpopular among northern European taxpayers.
An IMF spokeswoman confirmed that the Fund would be unable to lend more money to Greece unless it was sure that next year's financing gap would be filled.
"We never lend when we don't have an assurance that there will be no gap," said Caroline Atkinson at a briefing in Washington.
"That is how we maintain the safety of our members' money."
But a spokesman for Mr Juncker later said that if the EU and IMF inspectors currently in Athens could be convinced by new Greek austerity measures, there would be no problem with the next tranche of loans.