Russia says militants based in the Damascus suburb of Eastern Ghouta have promised to allow civilians to leave the enclave as Syrian troops are in the midst of an operation to drive out terrorists.
Russia has already introduced a daily ceasefire in the area but both Moscow and Damascus have said the militants have been preventing local residents from leaving.
On Monday, the Russian military said the militants had agreed to let civilians leave Eastern Ghouta in exchange for humanitarian aid.
The announcement came a day after Russia said militants had imposed a curfew during humanitarian pauses to prevent civilians from leaving the enclave.
Russia has designated four safe passage routes in Eastern Ghouta after a ceasefire was declared across Syria by the United Nations Security Council.
Eastern Ghouta has witnessed deadly violence over the past few weeks, with Takfiri terrorists launching mortar attacks on the Syrian capital in the face of an imminent defeat.
The Syrian army is making steady advances in the enclave, but it is facing a hostile West which is threatening airstrikes to stop the push.
A London-based monitor sympathetic to militants said Syrian government and allied forces pushed deeper into Eastern Ghouta Monday and have now retaken a third of the enclave.
Government forces "are advancing at a high pace because operations so far are mostly conducted in farmland," the so-called Syrian Observatory for Human Rights said.
According to the report, troops were two kilometers (1.2 miles) southeast of Douma, the main town in Eastern Ghouta, a semi-rural area that lies within mortar range of central Damascus.
Terrorists are using Eastern Ghouta as a launchpad for near-daily mortar attacks on the capital, which have killed many civilians and damaged residential houses.
The government lost control of Eastern Ghouta in 2012. Over the years, troops have clawed back nearly two thirds of the territory.
President Bashar al-Assad vowed on Sunday that Syrian forces would continue the latest campaign until the whole area is retaken.
His remarks came after army soldiers secured a humanitarian corridor for civilians to leave militant-held areas. Official news agency SANA said preparations were underway to deliver food to civilians trapped in Eastern Ghouta.