Debate over the rescue plan for Greece now shifts to the International Monetary Fund, which must decide whether it is willing to risk more money on a new bailout effort that the fund’s own analysis shows has a strong possibility of failing.

Greece may need “prolonged financial support” beyond the three years envisioned for the new bailout, the IMF concluded in a report distributed as part of recent negotiations in Brussels over the $172 billion rescue program.

The willingness of the IMF to continue lending to Greece is a critical part of the new program, because these loans would reduce the amount of money that Greece’s European neighbors must provide. Public sentiment in several countries has been turning against the Greek bailout, and some European leaders say they have provided as much support as their domestic politics will allow.

The statement released by European ministers early Tuesday morning in Brussels cited an “expectation that the IMF will make a significant contribution” to the new program. European official have said the amount may be around $17 billion, but agency officials have remained coy about the exact amount.

The IMF agreed to provide about 25 percent of the initial $140 billion bailout approved for Greece in May 2010 — far more than it has loaned to other nations in crisis. Members of the fund’s executive board have become increasingly concerned about the riskiness of lending more to Europe, wondering whether giving more support to Athens amounts to throwing good money after bad.

While the IMF board is unlikely to stand in the way of further lending to Greece, agency officials say the deal still needs to clear a series of hurdles in coming days if it is to comply with IMF rules. These rules require that the agency only provide loans for efforts that are fully financed and have a reasonable chance of success.

The IMF is still waiting on the completion of a debt restructuring deal in which private investors in Greek bonds will be asked to accept losses of 53.5 percent on the value of the bonds. European governments must also approve the new lending, and the Greek government must take several steps, such as overhauling local labor laws and finalizing a plan to put new public capital into the nation’s banking system.

In a statement Tuesday morning, IMF Managing Director Christine Lagarde said she would withhold any final decision on the loans until those conditions are met.

Lagarde said she would bring the issue to the board “as soon as the prior actions agreed with the Greek authorities are implemented and adequate financial contribution from the private sector is secured.”

The IMF analysis of Greece’s financial situation says the bailout faces “notable risks.” The analysis raises questions about Athens’ ability to resume borrowing money from investors in the years ahead and about whether the country’s total debt can be reduced over the next eight years to a manageable level.

In particular, the agency pointed to a “fundamental tension” in the Greek rescue effort: The steps being taken to improve the country’s public finances are pushing the economy further into recession, making the financial problems that much worse.

Still, the IMF sees the new rescue effort as a step in Europe’s halting efforts to return its financial system to normal.