PARIS—A Syrian government run by the country's main opposition group would cut Damascus's military relationship to Iran and end arms supplies to Middle East militant groups such as Hezbollah and Hamas, the group's leader said, raising the prospect of a dramatic realignment of powers at the region's core.

Burhan Ghalioun, the president of the Syrian National Council, said such moves would be part of a broader Syrian reorientation back into an alliance with the region's major Arab powers. Mr. Ghalioun's comments came Wednesday,...