The International Monetary Fund has made a package easing Greece's repayment burden a condition of its participation in a 86-billion-euro (USD 94-billion) bailout.
But several eurozone governments are dragging their heels, insisting on more evidence of debt-plagued Greece delivering on reforms as a condition of green-lighting the third rescue package of its kind since 2010.
"We will carry on working on this debt relief package," Lagarde said after talks on the issue on the sidelines of a meeting of G7 finance ministers and central bank governors in the southern Italian port of Bari.
The former French finance minister added that the IMF's position had not changed in the long-running saga.
"We have two issues, policies which are being voted on now, I hope, by the Greek authorities. Much progress has been made and we certainly hope that the Europeans will be far more specific in terms of debt relief, which is also an imperative."
Eurozone ministers agreed in principle last year to extend the repayment terms of part of Greece's debt if Athens delivered on pensions and tax reforms aimed at making the country's public finances more sustainable.
A decision on the shape of the relief package is required soon. Athens needs the first tranche of the bailout to be delivered by July to ensure it can repay seven billion euros (USD 7.6 billion) in maturing loans.
The issue is particularly sensitive in Germany, where the provision of debt relief to Greece is seen as a vote loser in the run-up to general elections in September.
On the other side of the debate, many economists have said a reluctance to write off some of Greece's debts has been counter-productive because of the negative impact deep cuts on public spending have had on economic activity.
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