The clash comes after Eurogroup president Jean-Claude Juncker announced Greece will be given an extra two-years to meet its debt reduction target of 120 per cent of GDP, with the deadline moving from 2020 to 2022.
He said: “The target, as far as the time-frame is concerned, has been postponed to 2022.”
According to The Telegraph, Lagarde was angered by the move as it breaches the IMF’s condition that Greek debt must become sustainable by 2020.
She said: “We clearly have different views. In our view the appropriate target is 120 per cent by 2020. It is critical that the Greek debt is sustainable.”
The debt sustainability target of 2020 was agreed as a condition of the IMF’s involvement in the second Greek bail-out package in March 2012.
Juncker added that finance ministers would have to meet again on 20 November to agree the final details on debt reduction and financing of Greek debt before paying the next tranche of the package.
The Greek government will need a further £26bn of international aid if its austerity programme is relaxed by two years, according to an as-yet unfinished EU-IMF troika report on Greece.