Six days of fighting in a Damascus suburb has killed more than a hundred people and possibly many more, activists said on Monday, in what the government also acknowledged may be a dramatic spike in the rising death toll in Syria.

President Bashar al-Assad’s forces pressed on with a major offensive against rebels closing in on parts of the Syrian capital, while government troops moved to encircle the contested town of al-Qusayr.

The precise number of those killed in the latest fighting in the Jdaidet Artouz and Jdaidet al-Fadel districts — the suburbs, around 15 km southwest of Damascus — could not be immediately confirmed.

The Britain-based Syrian Observatory for Human Rights said the death toll, mostly due to shelling, could be as high as 250.

The Local Coordination Committees, another activist group, put the death toll at 483.

It said most of the victims were killed in Jdaidet Artouz. State-run news agency SANA said Syrian troops had “inflicted heavy losses” on the rebels.

A government official in Damascus told The Associated Press that rebels were behind the “massacre” in Jdaidet al-Fadel.

The army also pressed on with its offensive near the Lebanese border, a strategic region because it links Damascus with the Mediterranean coastal enclave that is the heartland of Mr. Assad’s Alawi sect, an offshoot of Shia Islam.

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