AMSTERDAM—A new class of diabetes drug doesn't appear to increase patients' risk of heart attack, stroke or death, according to two large studies, offering some reassurance to doctors and patients concerned about possible negative heart effects.

But there was a signal in one of the trials—which were presented at an international cardiology meeting Monday—that the drug might increase patients' risk of heart-failure hospitalizations. Heart failure is a complex, chronic condition in which the heart doesn't pump enough blood to...