The Syrian Observatory for Human Rights said regime troops backed by fighters from Lebanon's Hezbollah movement were battling to recapture parts of the Wadi Barada region from rebels.
The area north of Damascus is the main source of water to the capital.
The Observatory, a Britain-based monitor of Syria's conflict, said regime forces had late on Wednesday launched "dozens of air strikes on parts of Wadi Barada along with artillery and rocket fire, killing a firefighter."
Fighting has continued in the area despite a nationwide ceasefire brokered by regime backer Russia and rebel sponsor Turkey, which has brought quiet to large parts of Syria.
The regime says forces in Wadi Barada include former Al-Qaeda affiliate Fateh al-Sham Front, previously known as Al-Nusra Front, which Moscow and Damascus say is excluded from the ceasefire.
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Rebels deny the group is in the area.
The capital's water supply has been cut since December 22, with the regime and rebels trading accusations over responsibility.
Regime forces late Wednesday also bombed several parts of rebel-held Eastern Ghouta near Damascus, while regime and loyalist forces battled Islamist militants there, the Observatory said.
The opposition-controlled Rashidin district on the western outskirts of Aleppo was also bombed, it said, killing a rebel fighter and wounding eight others.
The ceasefire agreement is meant to pave the way for peace negotiations later this month in the Kazakh capital Astana, but Ankara warned on Wednesday that violations of the truce by President Bashar al-Assad's government were putting the talks at risk.