In recent meetings, South Korean officials told their U.S. counterparts that continued White House inaction in Syria could embolden North Korea to use its own chemical weapons against its southern neighbor.

Similar messages were relayed by Turkish, Israeli and Saudi officials in recent days, telling President Barack Obama he must respond to Syria's alleged use of chemical weapons, current and former U.S. and Middle Eastern officials said. Failure to act, these allies said, could convince Iran that Washington isn't serious about...