WASHINGTON—The Pentagon is delaying a training program for Ukrainian soldiers so as to avoid giving the Kremlin an excuse to scrap the tenuous peace deal struck last month between Kiev and Moscow-backed separatists, a top U.S. general said Tuesday.

Lt. Gen. Ben Hodges, commander of U.S. Army in Europe, said U.S. officials wanted to make sure such training—which would involve U.S. military instructors deploying to western Ukraine—doesn’t “give the Russians an opportunity to say, ‘Look, the Americans are bringing in all these...