Syrian government troops have seized two towns, one of them an ancient Christian hamlet north of Damascus, as part of the military's offensive along the frontier with Lebanon, state media and activists say.

Syria's state news agency said that forces loyal to President Bashar al-Assad captured Sarkha early on Monday before also quickly sweeping rebels out of the nearby town of Maaloula.

The Lebanese TV channel al-Mayadeen, which closely follows the Syrian conflict, briefly broadcast footage that it said was from inside Maaloula, a predominantly Christian village, showing a cluster of buildings set in hilly terrain.

"The army has taken full control of Maaloula and restored security and stability. Terrorism has been defeated in Qalamoun [the region where Maaloula is located]," AFP news agency quoted a security official as saying.

The Britain-based Syrian Observatory for Human Rights, which has a network of activists on the ground, confirmed that both Sarkha and Maaloula had fallen to government forces.

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The seizure of the towns comes a day after Syrian troops backed by fighters from Lebanon's Shia Muslim group Hezbollah captured the nearby town of Rankous.

The push is part of an offensive that government forces have been waging since November in the Qalamoun area along the border with Lebanon.

Assad's troops have captured a number of rebel strongholds in region as they look to cut a vital opposition supply line across the frontier used to support rebels around the Syrian capital of Damascus.

Rebels seized Maaloula in early December, even as they were under fire from pro-Assad forces at the time.

The rebels included fighters of the Nusra Front, who abducted 12 Greek Orthodox nuns from their convent during the fighting. The nuns were released unharmed in March in exchange for the Syrian government releasing dozens of Syrian women from prison.

At the time, the abduction added to fears that Sunni Arab fighters were targeting Christians as the three-year Syrian conflict grows increasingly sectarian.

Source: Agencies