An Israeli offensive in Lebanon has the potential to increase the risk of a broader conflict that draws in Iran and Iran-aligned militants, particularly if Hezbollah's existence is threatened, the top U.S. general said on Sunday.

Air Force Gen. C.Q. Brown, the chairman of the Joint Chiefs of Staff, did not predict Israel's next steps and acknowledged Israel's right to defend itself. But he cautioned that a Lebanon offensive "can drive up the potential for a broader conflict."

"Hezbollah is more capable than Hamas as far as overall capability, number rockets and the like. And I would just say I would see Iran be more inclined to provide greater support to Hezbollah," Brown told reporters before stopping in Cape Verde on his way to regional defense talks in Botswana.