BEIRUT—Syrian regime forces and their Lebanese militia allies Hezbollah hit back at rebels around the capital Damascus following battlefield setbacks that have increased pressure on President Bashar al-Assad.

The Hezbollah fighters, reinforced by regime airstrikes, led a ground offensive to capture the rebel-held town of Zabadani, some 25 miles northwest of Damascus and about 7 miles from Syria’s border with Lebanon.

Video broadcast by Hezbollah’s media arm Al-Manar showed the Islamist group’s fighters in full military gear, including backpacks loaded with rocket-propelled grenades, running through what appeared to be scorched orchards on the outskirts of Zabadani. Explosions and the crackle of gunfire were heard in the background.

Al-Manar showed the town engulfed in smoke and several buildings in flames as Hezbollah and regime fighters in the surrounding hills pummeled the area with rockets and artillery shells.

“The artillery is playing the tune of the terrorists’ defeat at the gates of Zabadani,” said a voice-over on one of the videos, as Hezbollah appeared more determined than ever since the start of the Syrian war in 2011 to highlight its achievements and military prowess.