Michael Williams, the outgoing U.N. special envoy to Lebanon, said southern Lebanon has enjoyed relative stability for several years.
There have been minor skirmishes and border incursions by the Israelis, though the region has been relatively peaceful since the 2006 war between Hezbollah and Israel, he said.
Lebanese news outlet Naharnet reports that Syrian forces crossed into Lebanese territory and killed a 41-year-old Syrian national, the second such incident this week.
Williams said he "sincerely" hoped the violence in Syria would come to an end.
"I would also like to express my ardent wish for the realization of a vision for the region in which peace, including peace between an independent Palestine and Israel, can take hold and where democracy can flourish," he added.
While Lebanon was enjoyed relative stability, Williams said, the spirit of U.N. Security Council Resolution 1701, which brought an end to the Israeli-Hezbollah war, needed to be honored.
Both sides, he said, need to display "a stronger political will and take additional steps to allow us to move from a cessation of hostilities to a formal cease-fire."