The army says the injured include nine Lebanese soldiers. The officials say fighting broke out on Monday night and continued on Tuesday in the northern Lebanese city of Tripoli. They spoke on condition of anonymity because they are not allowed to speak to the media.
The mostly Sunni city also saw gun battles in May, when fighting over Syria killed eight people.
The latest clashes are between gunmen from a Sunni neighborhood and a rival district populated by Alawites, followers of an offshoot of Shiite Islam.
Assad is a member of Syria's Alawite minority. Rebels fighting his regime are members of the nation's Sunni majority.