The Lebanese militant group, a close ally to the Syrian government, issued the threat via its military media arm one day after American forces bombed pro-government forces in eastern Syria.
The Pentagon said yesterday the pro-government forces were infringing on a "de-confliction" zone established to protect US-backed local opposition forces, who are engaged in fighting the Islamic State group.
On its TV station al-Manar, Hezbollah broadcast footage it said was of an Iranian drone tailing an American one over eastern Syria.
Hezbollah's military media said it was only "self- restraint" keeping pro-government forces from attacking American units.
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Also today, a US official said the fight for Raqqa, the Islamic State group's de facto capital, will "only accelerate" as the militants lose their grip on Iraq's Mosul.
Brett McGurk, the US envoy for the global coalition against IS, said the US and its local allies, the Kurdish-led Syrian Democratic Forces, were prepared for a protracted fight for the northern Syrian city. He spoke at a press conference in Baghdad.
McGurk said the fight for Raqqa will be a "difficult and very long-term battle.