Some 393,000 people are trapped in the enclave near Damascus, which has been besieged by the government since 2013.
Since then, more than 500 civilians have been killed, including women and children, according to local activists.
"Russia is daily undertaking efforts to ensure a cessation of hostilities, for humanitarian pauses to be established, to alleviate the plight of suffering civilians", he told council members.
What is happening on the ground?
Last week Syrian government forces launched an operation to take control of Eastern Ghouta.
Fighting was reported by monitors including the United Nations after the Russian-ordered pause began at 09:00 local time.
Lowcock said trucks loaded with supplies have been poised to go to 10 locations since Saturday - but there has been no access for humanitarian convoys, nor authorisation by the regime to go into the besieged areas.
The World Health Organization said it had a list of more than 1,000 critically sick and wounded people who urgently needed to be evacuated.
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No civilians have left eastern Ghouta since the humanitarian pause began Tuesday. Ten people were also reported injured in Misraba. "All attacks were successfully repelled by government forces", Zolotukhin told reporters. "Militants still do not observe the ceasefire and do not allow the civilian population to leave the risky area", Zolotukhin said.
A five-hour "humanitarian pause" has been held in a rebel-held enclave near the Syrian capital Damascus, which saw government and Russian forces set up a corridor to allow civilians to leave.
"I think either Russian Federation has to admit that it's not capable or it doesn't want to play a role in ending the Syrian conflict here", Votel added, saying, "I think their role is incredibly destabilizing at this point".
What was supposed to happen?
The actions of the terrorists operating in eastern Ghouta, which is a current hotspot in the Syrian conflict, indicate their unwillingness to follow resolutions and their desire to continue warfare, the head of the Reconciliation Center said.
Residents would be informed via leaflets, text messages and videos, it added.
Ingy Sedky with the global Red Cross says that for a humanitarian corridor to work, it needs to be well planned and implemented with the consent of all parties in the conflict.
Wednesday's ground assault targeted the Hawsh al-Dawahra area at the eastern edge of the enclave.
Mark Lowcock, the United Nations under secretary-general for humanitarian affairs, said there has been no change in the situation around the rebel-held enclave in the Damascus suburbs despite a ceasefire resolution Saturday. "The violations of the truce are constant - 24 hours a day", Aboud said.
Regime-backer Russian Federation on Monday announced five-hour halts in the bombardment of the enclave and said it was guaranteeing civilians safe passage to flee.