Elsewhere, at least 30 people, including six civilians, were killed in some of the heaviest US-led air strikes yet on the Islamic State (IS) group in Syria.
And the jihadist group carried out a double car bomb attack that killed 11 people in northwestern Hasakeh city, where regime forces have been fighting to fend off an IS assault.
Syrian state television and Hezbollah's Al-Manar station announced the advance into Zabadani on Sunday, a day after a major operation against it began.
"Operations are continuing with dozens of terrorists killed and wounded."
The Syrian Observatory for Human Rights said regime forces and Hezbollah had entered Zabadani and intense clashes were underway in its east and west.
Army helicopters dropped at least 22 barrel bombs on the town and were also shelling it heavily, said the Britain-based monitoring group.
At least 14 pro-government and Hezbollah fighters had been killed in the past 24 hours, along with at least 12 rebels and a civilian, it added.
Zabadani was one of the first towns to fall into rebel hands, in early 2012, and is now the opposition's only remaining stronghold along the Lebanese border.
The town is strategically important for the regime in part because of its proximity to the capital and the highway that runs from Damascus to Beirut.
Zabadani has been under siege for more than a year, and most of the civilians have already fled, according to activists.
Alwan, an activist from Zabadani who now lives outside Syria, said there were still thousands of civilians in the east of the town and many wounded people.
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