The regime advances in Eastern Ghouta came as a monitor reported more than 350,000 people killed in Syria's war, and as hundreds fled a Turkish-led advance in the northern area of Afrin, where a Kurdish-majority city is also under threat of being besieged.

Syria's civil conflict enters its eighth year this week with fighting on several fronts, but the assault on Eastern Ghouta has been one of the most ferocious of the war.

Since February 18, forces loyal to President Bashar al-Assad have retaken nearly 60 percent of the enclave, whittling down rebel territory to three isolated pockets.

Backed by Russia, the advance has battered Eastern Ghouta with air strikes, artillery and rocket fire, raising widespread international concern and prompting urgent calls for a ceasefire.

France's envoy to the United Nations, Francois Delattre, on Monday urged Moscow to put pressure on its ally to halt the offensive, saying: "Russia can stop the bloodbath."

Pro-regime forces advanced again on Monday, heavily bombing two rebel-controlled towns closest to the capital, said the Syrian Observatory for Human Rights.

Air strikes and rocket fire slammed into the towns of Harasta and Arbin, the Britain-based monitor said, as the regime used the recently recaptured town of Medeira nearby as a launching pad for a ground assault.

Syrian state media also reported a government advance in Ghouta, seizing the town of Efteris to the south.

The other two areas still in rebel hands are Douma, the region's biggest town in the north of the enclave, and the zone around Hammuriyeh and other towns to the south.

- Queueing for meat -

An AFP correspondent in Douma said the morning was relatively quiet, allowing civilians to venture out of bomb shelters to check on the destruction in their homes or gather food.

Residents were seen queueing at a butcher shop, whose owner had slaughtered a calf that he could fatten up no further because there was nothing left to feed it.

Syria's conflict broke out in March 2011 with peaceful protests against Assad, but a regime crackdown paved the way for a fully-fledged war.

At least 353,935 people have died since, including more than 106,000 civilians, the Observatory said on Monday, providing a new overall death toll for the conflict.

More than 19,800 children are among the dead, it said.

UN children's agency UNICEF on Monday reported a 50 percent increase in the number of children killed in the conflict last year, condemning "extreme and indiscriminate violence".

In the Ghouta offensive alone, at least 1,162 civilians have been killed, including 241 children, the Observatory said in a new toll on Monday.

More than 35 civilians have also been killed in rebel fire on government-controlled zones in Damascus and its outskirts since the start of the Ghouta offensive, according to the Observatory.

Rebel mortar and rocket fire killed two civilians on Monday, according to state news agency SANA.

Even before the offensive began, rebel-held parts of Ghouta were facing a crippling government siege that made food and medicine hard to access.

The United Nations on Monday said more than 1,000 people in Eastern Ghouta needed urgent evacuation from the area for treatment.

"The majority of them are women and children," said Linda Tom, from the UN's humanitarian coordination office (OCHA) in Damascus.

Last month, the UN Security Council demanded a month-long ceasefire to allow aid deliveries and medical evacuations, but no such evacuations have taken place.

- Hundreds flee Afrin -

Syrian troops have used siege tactics on several areas around the capital, sealing off rebel-held territory and pressing a military operation before securing an evacuation deal.

A similar deal has been put forward for parts of Eastern Ghouta, including the town of Hammuriyeh, a negotiator and the Observatory told AFP.

The agreement would offer safe passage to rebels and civilians who wanted to leave and the town would come under government control.

The Observatory confirmed talks were taking place on Hammuriyeh, as well as the towns of Kafr Batna, Jisreen and Saqba, but said no agreement had yet been reached.

All three towns are controlled by Islamist rebel group Faylaq al-Rahman, which has repeatedly denied engaging in talks with the regime.

Since the conflict broke out seven years ago, an array of world powers have become involved, including Turkey.

For weeks, Ankara and allied Syrian rebels have pursued an offensive against Afrin, a Kurdish-controlled region of northwest Syria.

Hundreds of residents were seen fleeing the city of Afrin on Monday, with the Observatory reporting more than 2,000 arriving in an area controlled by pro-regime forces.

Hundreds more were on the road, it said, after Turkish forces and their allies on Saturday arrived to within less than two kilometres (one mile) of the city, sparking fears it could be besieged.