WASHINGTON—President Barack Obama said on Saturday he has decided he should order a limited military strike against Syria, but in a move laden with political and diplomatic implications, he agreed in an about-face to solicit authorization for the mission from Congress.

Mr. Obama's announcement in a Rose Garden statement brought an unusually sudden halt to a military mobilization that for days had appeared on the cusp of a bombardment of Syria as punishment for its alleged use of chemical weapons on Aug. 21 that killed more...