Air strikes shook a besieged rebel-held town east of the Syrian capital on Monday, sparking fears among civilians of a fate similar to battered Aleppo city.

More than a dozen raids and several mortar rounds pounded Douma in the Eastern Ghouta opposition stronghold near Damascus, said the Syrian Observatory for Human Rights monitoring group.

The bombardment is part of a five-month offensive by government forces that has "chipped away at opposition territory" there, Observatory head Rami Abdel Rahman told AFP.

Backed by allied militia, Syria's army has advanced to just three kilometres (two miles) east of Douma, the largest rebel-controlled town in the area and the focus of the latest military push, he said.

AFP's correspondent in Douma said he counted 10 strikes at least on Monday morning alone.

The bombardment forced schools to shut down, just a week after the start of the new academic year, while streets emptied and shops closed.

Activists said Douma residents were concerned that Monday's air strikes were a prelude to a ground offensive much like the army's current push to take all of Aleppo city.

"People don't know what will happen to them -- anything is possible. We could become like eastern Aleppo," said Douma-based activist Mohammad.

The army of President Bashar al-Assad announced a major push on September 22 to capture Aleppo's opposition-held east and has gained ground in the city with the help of ally Russia.

The activist told AFP he and other residents "are bracing themselves for the worst" and scrambling to prepare underground bomb shelters and stockpile medical supplies.

Douma has been under government siege since 2013 and is a bastion of the powerful Jaish al-Islam (Army of Islam) rebel group.

In June, aid agencies reached Douma for the first time in three years, bringing in desperately-needed food and medical aid.

But a doctor in Douma warned that supplies are running out.

A ground offensive would cause many casualties and be a burden for hospitals, said doctor Mohammad Abu Salem. "The warehouses where we keep our medical supplies are practically empty," he said.

Abu Anas, a father of four who works in a grocery shop in Douma, said the government had seized farmlands east of the town.

"As the regime advances and tightens the noose around us, the supply of goods in Eastern Ghouta has plummeted," he said.

More than 300,000 people have been killed since Syria's conflict erupted in March 2011 with anti-government protests.