BEIRUT — Airstrikes by Syrian jets and shells from tanks leveled a neighborhood in a restive city near the capital of Damascus on Tuesday, killing 18 people, and at least five rebel fighters died nearby in clashes with regime troops, activists said.

The airstrikes on the city of Douma, northeast of the capital, left residents scampering over a huge expanse of rubble and using their hands to dig up mangled bodies, according to activist videos posted online.