Opposition sources denied there was any such deal, but a source inside the Wadi Barada region reported several hundred civilians were leaving under an agreement.
Wadi Barada, some 15 kilometres northwest of Damascus, provides most of the water to the capital, but mains supplies have been cut since December 22, causing shortages for millions.
President Bashar al-Assad said this week he was determined to retake the area and secure the water supply, and fighting has continued there despite a nationwide truce in place since December 30.
"The agreement that was reached in principle requires the militants to give up their heavy weapons and for non-local militants to leave the area of Wadi Barada," he said.
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"(Then) the Syrian Arab Army will enter the area to clear it of mines and bombs to prepare for the entry of maintenance teams... To fix the damage caused to the water pumps and pipes by the terrorists' attacks."
But Ahmed Ramadan, an official with the opposition National Coalition, denied any such deal had been reached.
The Syrian Observatory for Human Rights, a Britain-based monitor of the war, also said the government had not reached a comprehensive deal with rebels.
But it reported that residents wishing to leave were being offered safe passage on an individual basis.
And a source on the ground in Wadi Barada said today that some 600 civilians had left, passing through a makeshift tent where government officials were checking documents.
Syria's government accuses rebels, including former Al-Qaeda affiliate Fateh al-Sham Front, of deliberately cutting the supply to the capital.
The government has concluded dozens of so-called "reconciliation deals" with rebel-held areas in Syria in recent months, particularly around the capital.
The deals usually offer civilians and rebels safe passage to opposition-held territory elsewhere in exchange for surrendering the area to the army.
The opposition says it is forced into such deals by government sieges and assault, and terms them a "starve or surrender" tactic.