Greece's efforts to close its budget gap have gone a long way but are "not sufficient," International Monetary Fund managing director Christine Lagarde said.
Lagarde also said that the turmoil that has raised fears of an Italian financial meltdown is "essentially market driven."
"Some of the Italian numbers are excellent," she told reporters, adding that "It is clearly a fact that Italian growth has to improve."
With debt costs shooting up Monday for both countries and worries that a contagion would spread to more of Europe's weaker peripheral economies, Lagarde said Fund officials were on the ground in Brussels trying to help eke out a deal to stabilize Greece's finances with the region's finance ministers and bankers.
"Greece has done a lot of work to reduce deficits and achieve fiscal consolidation in the range of five percentage points of GDP; this is a significant achievement." she said.
"Equally, we all know this is not sufficient, that more work needs to be done."
Lagarde's comments, made at the beginning of her second week as head of the world's crisis lender, came as new worries in Europe sent stock markets plunging and debt cost soaring for Italy and Spain, the eurozone's third and fourth largest economies.
Lagarde downplayed Italy's problems.
"The primary deficit of Italy is one of the lowest," she said, referring to its basic balance of government operating expenditures versus income.
She described the country's high government debt as having "very particular characteristics" -- noting the fact that most of it is held inside the country.
But she said that Italy needs to implement already-agreed fiscal consolidation and austerity measures to reduce the country's deficit.
Bringing the deficit down to three percent of GDP in 2012 "is essential to restore the situation of Italy" she said.