Speaking on French radio, Lagarde was asked whether the rescue plan for Greece clinched in Brussels on Monday was viable without restructuring Athens's enormous debt load.
"The answer is fairly categoric: 'no'," she insisted.
She said Greece's European partners had accepted the "principle" of easing the debt burden, but "neither the amount nor the method."
"For us to participate, we need a complete programme and from our point of view, this programme has two parts," she told Europe 1.
The first part is that the Greeks must enact fundamental reforms to free up the economy and allow it the possibility to grow.
(IMF head Christine Lagarde. Photo: AFP)
"The second part comes from the lenders, and that consists on one hand of providing finance and on the other hand of restructuring the debt to ease the burden," she said.
She said she preferred to extend the maturity of the debt and also stretch out a grace period during which Athens is not obliged to make payments.
Lagarde also said the interest payments should be reduced to the minimum amount "to make the debt sustainable."
On Wednesday, the Greek parliament passed a sweeping and unpopular set of reforms demanded by creditors in return for an 86 billion euro ($94 billion) rescue package.
Chancellor Angela Merkel on Friday acknowledged that the contentious deal was "hard" for all sides, as she urged the German parliament to vote in favour of the agreement.