Christine Lagarde, the head of the International Monetary Fund, said Thursday that she counted on euro-zone countries to support the Greek effort to bring down its debt to sustainable levels.

Talking to reporters in Washington, Lagarde said the Europeans have promised to “consider any additional measures and assistance needed” as long as that Greece delivers on its commitments.

“What form those further measures and assistance will take will certainly be discussed at a later stage,” she added.

Together with the European Commission and the European Central Bank, the IMF is providing emergency loans to Greece after a sovereign debt crisis threatened to lead to the default of the euro-zone country. In a report published Wednesday, the IMF identified a potential financing gap of $14.5 billion on Greece’s program.

The managing director of the IMF said Thursday that Greece has made considerable efforts to comply with its program commitments. “Not all of them have been delivered upon, but there has been considerable effort and results,” Lagarde said.

Asked whether Germany, which is resisting calls for further debt relief for Greece, could change its position after its federal elections in September, Lagarde said she had “no reasons to believe that the Europeans” would back out of their promises to Greece and third parties, such as the IMF.

The sustainability of Greek debt was openly put into question this week by Brazil’s representative to the IMF, Paulo Nogueira Batista, who criticized the executive board’s decision to release $2.25 billion of rescue loans to Greece and abstained from the vote.

The incident undermined the positive tone of the IMF’s report on Wednesday and led to the recall of Batista to Brazil. Guido Mantega, the Brazilian finance minister, assured Lagarde that Batista’s actions were not authorized by the Brazilian government, and that if a vote could be retaken, Brazil would support the Greek program.

Lagarde said she was “very pleased that the position of Brazil could be rectified and clarified at the highest level.”

On internal matters, Lagarde appeared hopeful that a reform of the IMF’s voting system is still possible by the end of this year, even though the United States hasn’t yet given its support to it. The proposed reform would increase the representation of emerging economies to better reflect their increasing share of the world economy.

“There’s still one big vote missing,” Lagarde said, but “plan A has to be completed. It’s a matter of representation and delivering on commitments.”

An IMF report published Thursday estimated that if the five systemically important economies –the United States, China, the euro zone, Japan and Britain -- operated closer to their potential, global growth would be 3 percentage points higher. Lagarde noted that this is “not insignificant,” given the fact that growth is “not as vigorous as expected.”

The report underlines the risks of a “messy unraveling,” when the U.S. Federal Reserve starts to withdraw its monetary stimulus, and of incomplete fiscal and structural policies. It warns that these include “protracted low growth and sovereign debt stress.”

Lagarde also urged China to keep its banks and shadow banking system under scrutiny. In a separate report published Thursday, the IMF calculated that China’s exchange rate is undervalued by 5 percent to 10 percent.

Asked whether she supported Fed Vice Chairwoman Janet Yellen to succeed Chairman Ben S. Bernanke, Lagarde responded positively: “She’s my friend, I’ll say no more. And she is a very competent woman.”