WASHINGTON—A senior International Monetary Fund official Wednesday said it can’t help Europe with fresh emergency financing for Greece because Athens’s creditors haven’t yet committed to detailed debt relief.

The comments show that the agreement touted by European finance ministers last night to release fresh bailout cash for Greece hasn’t nailed down the key elements the IMF says are critical to finally return the debt-laden country to health. Rather, the IMF’s reserved support for the deal has paved the way for Germany to...