BEIRUT, Lebanon — Syrian government forces and their allies in the Lebanese Shiite group Hezbollah started a new offensive Saturday against insurgents in Zabadani, a mountain town near the border with Lebanon that was one of the first to be wrested by rebels four years ago.

Hezbollah’s news channel, Al Manar, showed smoke rising from Zabadani and said that the government forces were attacking from several directions and that heavy airstrikes and shelling were continuing.

Mortar shells hit several central neighborhoods in Damascus, the Syrian capital, as insurgents appeared to strike back, residents said. The Syrian state news agency reported that one person had been killed and two wounded when a shell hit the Dama Rose Hotel, which often hosts dignitaries.

The assault comes a day after insurgents began a major offensive in the divided city of Aleppo in the north near the border with Turkey, and after weeks of fighting in the Qalamoun mountains farther north along the border with Lebanon, where Hezbollah has played a leading role. The government is seeking to maintain and strengthen control over the border area and the crucial Damascus-Beirut highway.