WASHINGTON—The U.S. and its regional allies agreed to increase shipments of weapons and other supplies to help moderate Syrian rebels hold their ground and challenge the intervention of Russia and Iran on behalf of Syrian President Bashar al-Assad, U.S. officials and their counterparts in the region said.

The deliveries from the Central Intelligence Agency, Saudi Arabia and other allied spy services deepen the fight between the forces battling in Syria, despite President Barack Obama’s public pledge to not let the conflict...