As the White House has soured on Israel's war with Hezbollah in Lebanon, U.S. President Donald Trump has shocked many in the region by pushing an alternative: Let Syria fight the Iran-backed militant group instead.

He has suggested that the battle-hardened and Islamist-led insurgents who overthrew Syria's autocratic President Bashar Assad a year and a half ago and formed a new government would do a better job of rooting out Hezbollah than the Israeli army.