FRANKFURT — The International Monetary Fund threatened to withdraw support for Greece’s bailout on Tuesday unless European leaders agree to substantial debt relief, an immediate challenge to the region’s plan to rescue the country.

The aggressive stance sets up a standoff with Germany and other eurozone creditors, which have been reluctant to provide additional debt relief. The I.M.F role is considered crucial for any bailout, not only to provide funding but also to supervise Greece’s compliance with the terms.

A new rescue program for Greece “would have to meet our criteria,” a senior I.M.F. official told reporters on Tuesday, speaking on the condition of anonymity. “One of those criteria is debt sustainability.”

Debt relief has been a contentious issue in the negotiations over the Greek bailout.

Athens has pushed aggressively for creditors to write down the country’s debt, which now exceeds €300 billion. Without it, Prime Minister Alexis Tsipras has argued the debt will remain a heavy weight on Greece’s troubled economy.