ESPARGOS, Jun. 23 (Reuters) - 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 General 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.

"Again, all this could help to broaden the conflict in the region and really have Israel not only be worried about what's happening on their southern part of the country, but also now what's happening in the north."

Brown's comments came as Israeli Prime Minister Benjamin Netanyahu said on Sunday that a coming end to the intense phase of fighting in Gaza would allow Israel to deploy more forces along the northern border with Lebanon.

Iran-backed Hezbollah began attacking Israel shortly after Hamas' Oct. 7 assault sparked the war in Gaza, and the sides have been trading blows in the months since then. Hezbollah has said it would stop until there is a ceasefire in Gaza.

Earlier in June, Hezbollah targeted Israeli towns and military sites with the largest volleys of rockets and drones in the hostilities so far, after an Israeli strike killed the most senior Hezbollah commander yet.

Brown's remarks came as Israeli Defence Minister Yoav Gallant headed to Washington on Sunday to discuss the next phase of the Gaza war and escalating hostilities on the border with Lebanon.

Brown noted that the United States could be more limited in its ability to defend Israel from attacks by Hezbollah than it was helping intercept Iran's April missile and drone attack on Israel, which was largely thwarted.

"From our perspective, based on where our forces are, the short range between Lebanon and Israel, it's harder for us to be able to support them in the same way we did back in April," Brown said.

Photo from Reuters