DAMASCUS, Syria—Syrian army units and other forces loyal to President Bashar al-Assad stepped up their offensive on Thursday against several towns outside Damascus, after Islamist factions controlling the communities rejected the government's truce offers.

Rebels responded to the fresh offensive by showering government-controlled sections of Damascus with mortar shells, in barrages that have killed 14 people and wounded nearly 50 others since Wednesday, according to city police officials.

...