Rebels fighting under the Free Syrian Army banner in Wadi Barada warn the fragile ceasefire is in danger of collapse.
Syria's army advanced on Monday, as it battles to capture a rebel region that is key to the capital's water supply, launching air strikes and artillery fire that threatens a fragile nationwide truce.
The ceasefire brokered by ally Russia and Turkey, which backs the opposition, is now in its fourth day, despite sporadic violence and continued fighting in the Wadi Barada area near Damascus.
"Regime forces and fighters from Lebanon's Hezbollah group are advancing in the region and are now on the outskirts of Ain al-Fijeh, the primary water source in the area," said Rami Abdel Rahman, director of the UK-based Syrian Observatory for Human Rights monitor.
He said government troops and allied fighters were engaged in fierce clashes with rebels, including from the former al-Qaeda affiliate now known as Jabhat Fateh al-Sham.
The monitor said government forces were carrying out air strikes and artillery fire on the area, northwest of the capital, but reported no casualties.
Wadi Barada has been surrounded by government forces since mid-2015, but the siege was tightened in late December as the army piled on pressure seeking to secure a "reconciliation" deal.
It has won several of these deals in opposition areas around the capital, offering safe passage to surrendering rebels in return for retaking territory.
The opposition criticises them as a "starve or surrender" tactic.
As the fighting stepped up in the area, Syria's government said rebels damaged key water infrastructure, causing leaking fuel to poison the water supply and then cutting it off altogether.
The United Nations says at least four million people in Damascus have been without water since December 22.
The Syrian Observatory said about 1,000 civilians - all of them women and children - fled the fighting in Wadi Barada over the weekend, moving to other parts of the province.
The violence threatens the delicate truce that came into force last week and is intended to pave the way for new peace talks in Kazakhstan later this month.
Four civilians and nine rebels have been killed since the truce began, but officially it is still holding.
In a statement, rebels fighting under the Free Syrian Army banner in the Wadi Barada warned the truce was in danger of collapse.
"We call on the sponsors of the ceasefire agreement to assume their responsibility and pressure the regime and its allied militias to stop their clear violation of the agreement," the statement said.
Otherwise, they warned, "we will call on all the free military factions operating inside Syria to overturn the agreement and ignite the fronts in defence of the people of Wadi Barada"
The statement said Wadi Barada was included in the deal brokered by Moscow and Ankara and accused the regime of violating the agreement.
The ceasefire deal, and the plan for new talks, received the unanimous backing of the UN Security Council on Saturday, despite offering a competing track to UN-sponsored negotiations.
Turkey and Russia are organising the talks in Astana along with ally Iran, and say they are intended to supplement, not replace, UN-backed negotiations scheduled to resume in February.
Despite backing opposite sides in Syria's conflict, Ankara and Moscow have worked closely in recent months on the war, brokering a deal to evacuate civilians and surrendering rebels from Aleppo last month before the regime recaptured the northern city in full.