Regime warplanes pounded Eastern Ghouta including the main town of Douma early Tuesday, as well as the towns of Sabqa and Hammuriyeh overnight, the UK-based Syrian Observatory for Human Rights monitor said.
"The Russian Reconciliation Centre guarantees the immunity of all rebel fighters who take the decision to leave Eastern Ghouta with personal weapons and together with their families", said the defense ministry statement.
Zolotukhin said anti-government fighters and their families are being allowed passage during certain hours in the daytime.
Fresh air strikes batter several key towns despite the daily "pause" announced by Russian Federation.
"The situation is catastrophic", said a doctor speaking from the rebel pocket.
Eastern Ghouta's around 400,000 residents have lived under government siege since 2013, facing severe shortages of food and medicines even before the latest offensive began.
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Those include 24 people who were killed in government attacks on Tuesday, AFP said.
According to the report, an air strike by a "Russian fixed-wing aircraft" last November hit a market and killed at least 84 people just west of Aleppo in a so-called "de-escalation zone" that was declared by Russia, Iran and Turkey.
The United Nations says another attempt is planned for Thursday.
In their 15th report, published Tuesday, the investigators also accused a US-led coalition of breaching global humanitarian law with a deadly strike a year ago on a school near the Islamic State group's former stronghold of Raqa.
Pawel Krzysiek, head of communications for the International Committee of the Red Cross in Syria, posted a video after the aid convoy returned, detailing what he and the other team members witnessed. The goal of the operation is clear Turkey's Syrian border from the terrorist threat.
A humanitarian aid convoy reached East Ghouta for the first time in weeks on Monday, but was forced to return to Damascus before all supplies were unloaded due to "constant shelling and ongoing fighting", Ingy Sedky, an ICRC spokeswoman told Syria Direct on Tuesday.
Syria has established a humanitarian corridor to allow civilians to leave the operation zone, while Russian Federation has been enforcing daily pauses in fighting from 09:00 a.m.to 02:00 p.m. local time to facilitate the exit of people.