The ground attack was launched in defiance of a U.N. Security Council resolution to halt what Secretary-General Antonio Guterres called "hell on earth", and in spite of Russia's plan for a daily humanitarian pause in airstrikes.
The Reconciliation Center also urged the militants to stop holding the civilians hostage in the besieged area and allow them to leave.
The United Nations Human Rights Council on Friday was set to hold an emergency session on Eastern Ghouta at the request of Britain.
With no sign of decisive worldwide pressure to stop the attack, eastern Ghouta seems likely to meet the same fate as other areas won back by the government, where humanitarian corridors eventually became escape routes for defeated rebels.
A Russian plan for a five-hour pause in fighting in Syria's eastern Ghouta needs to be expanded to allow aid deliveries to enter and civilians and urgent medical cases to leave, United Nations officials said on Thursday.
They also fear their region could meet the same fate as the eastern, rebel-held half of the city of Aleppo, where a similar Russian-ordered pause in 2016 called on residents to evacuate the area and for gunmen to lay down their arms.
With a failed cease-fire, Russia's commitment to de-escalate violence and negotiate a political solution is questionable.
The preliminary analysis conducted by UNOSAT of satellite imagery from eastern Ghouta's towns of Kafr Batna and Arbeen shows new damage in a 62.5-square-kilometer (24-square-mile) area, with buildings completely destroyed or damaged since December 3. Moscow's intervention on behalf of the Syrian government, which began in 2015, has been instrumental in turning the tide in favour of president Bashar Al Assad.
"The sweeping propaganda campaign waged by Washington, blaming Russian Federation for failing to fulfill its obligations in Syria, suggests that it is not care for civilian Syrians, but a cold-blooded political premeditation that is behind it: to keep an enclave of extremists by all means in the suburb of the Syrian capital", the embassy said.
A senior World Health Organization official told Reuters on Friday that 84 patients including children in Eastern Ghouta were the top priority for medical evacuations among 1,000 sick and wounded needing treatment.
It is, however, the more "conventional" weapons that have caused most of the deaths in eastern Ghouta.
Nauert said the ceasefire resolution adopted by the UN Security Council (USNC) Saturday is "clearly not working", and more than 100 people were killed since then.
The ambassador said they have killed hundreds of civilians, inducing government forces to respond to protect the civilians against terrorism.
The people in the capital are still preferring to stay indoors, particularly in the eastern Damascus' neighborhoods close to Eastern Ghouta.
However, they are generally silent on daily mortar attacks on Damascus, which take the lives of civilians.
Turkey's military says eight of its soldiers were killed in its offensive on a Kurdish-held enclave in northwestern Syria.
The eastern suburbs-a cluster of several towns and villages on Damascus' eastern edge-have faced a deadly and brutal onslaught for weeks by Syrian regime troops, backed by Russian Federation.