The main rebel group in the southern pocket of Syria's opposition-held Eastern Ghouta has said it is negotiating with a United Nations delegation about a ceasefire, aid and the evacuation of urgent medical cases.

"We are engaged in arranging serious negotiations to guarantee the safety and protection of civilians," said a spokesman for Failaq al-Rahman.

"The most important points under negotiation are a ceasefire, ensuring aid for civilians and the exit of medical cases and injured people needing treatment outside Ghouta," he said.

But a general evacuation of civilians and rebels was not on the table, he added.

In a month-long assault, pro-Syrian government forces have marched into much of Eastern Ghouta, the last major insurgent bastion around Damascus.

Troops have splintered Ghouta into three besieged zones in one of the bloodiest offensives of the seven-year war, with rebels facing their worst defeat since the battle of Aleppo in 2016.

A number of patients requiring urgent medical attention have been evacuated from the northern pocket and some aid has entered there.

This has not yet happened in the southern pocket.

Figures close to the two main rebel groups – Failaq al-Rahman in the south and Jaish al-Islam in the north – have said discussions are underway for the transfer of Failaq al-Rahman and Jaish al-Islam fighters to opposition held areas in northern and southern Syria respectively.

Shelling and ground battles have resumed this afternoon across Eastern Ghouta, the Syrian Observatory for Human Rights said.

The United Nations office for the coordination of humanitarian affairs (OCHA) said on Thursday at least 20,000 people had left Eastern Ghouta in the past week, most from the southern pocket through the Hammouriyeh area.

The Observatory said about 50,000 had left the southern pocket in the past 72 hours and thousands left today.

President Bashar al-Assad has visited army positions in Syria's Eastern Ghouta, Syrian state media reported.

The Syrian army opened a corridor near Hammouriyeh this week and civilians have been making their way out towards army positions on foot, hauling their belongings with them.

OCHA said conditions for those remaining in Eastern Ghouta are "dire".

"There is limited food, with reports of the usual ration of bread for one day being consumed over the period of a week to 10 days; insufficient sanitation and hygiene support for those living in basements, and increased risk of communicable disease," it said.

State TV said the Syrian army had given a group of rebels in another pocket, the smaller Harasta area, an ultimatum to withdraw.

An opposition official from Ghouta privy to the negotiations told Reuters a delegation had left Harasta and was working out the terms of a deal that would follow previous surrender accords for rebel-held areas subjected to bombardment and siege.

This afternoon he said there was an agreement in principle and it would be enacted within 24-48 hours.

Local rebels were offered two choices - either to leave to opposition areas in northern Syria or settle their situation and become part of local pro-government militias that would maintain security.

Other terms of the deal would ensure that they handed over their weapons, he added.