"The cabinet offers its deepest and sincerest condolences to the Syrian people and to the family and relatives of the martyr," SANA quoted the cabinet as saying on Saturday.
According to the state-run news agency, Saleh was shot dead on Saturday in Quneitra near the occupied city of Majdal Shams, by an Israeli soldier.
Saleh had spent 12 years in jail in Israel until his release in 1997. He then fled to Syria where he served as a member of the Syrian parliament.