The International Monetary Fund could sign on to a deal between Greece and its creditors before debt relief measures it demands have been agreed, director Christine Lagarde said Tuesday.

"There can be a programme in which the payment does not take place until debt measures have been clearly defined by the creditors," she told German business daily Handelsblatt.

Her proposal to agree on the outline of a programme including the IMF, but withholding disbursement of funds until debt relief details are nailed down, is similar to one proposed at the Eurogroup meeting of eurozone finance ministers last month which ended without an agreement.

Talks over Greece's debt mountain -- which stands at 179 percent of GDP -- have been paralysed in recent weeks by disagreements between the IMF and European creditors led by Germany.

The Europeans expect Greece's economy to grow strongly and its government to bring in large surpluses in revenue in the coming years, allowing it to pay down its debts.

But the IMF is less optimistic, arguing there must be further debt relief for Athens before it can label its debt sustainable and justify loaning Greece any more cash.

Lagarde does not believe the total amount of Greece's debt must be reduced, but calls for a "significant extension" of the payment period and a delay on interest payments.

German leaders are reluctant to offer yet more unpopular debt relief ahead of elections in September, but have also promised lawmakers that the IMF will remain on board.

They say any discussion about debt relief must take place after the end of the 86-billion-euro ($96.7 billion) third bailout programme agreed in 2015, which runs until the middle of next year.

Pressure is on to reach a deal so that Greece can make a payment of around 7.5 billion euros that falls due in July.

"If the creditors haven't reached a point where they can accept and respect our forecasts, if they need more time to get there, then we can admit that and give them a bit more time," Lagarde said.

May's Eurogroup gathering ended without an accord, but all sides remain keen to avoid a repeat of the 2015 impasse that almost saw Greece pushed out of the euro.

The European Central Bank last week called for creditors to create "clarity" at their next meeting on June 15 by striking a deal restoring investors' confidence in Athens -- allowing the Greeks to turn to financial markets for cash in future.