In East Ghouta, where recently the Syrian and Russian authorities established a five-hour humanitarian truce every day, the Damascus Army and its allies face extremist groups, which occupy that large area since 2012.
A spokesman for Jaish al-Islam, one of the two main insurgent groups in Eastern Ghouta, said rebels had repelled the Mesraba attack.
On Friday a United Nations convoy was able to successfully deliver aid to the area, after previous deliveries were halted by shelling.
Almost 950 civilians have been killed since Russia-backed government forces launched a blistering assault on the last opposition bastion near Damascus on February 18.
Takfiri groups in eastern Ghouta deny this, but eyewitnesses on Friday saw gunfire and mortar fire from inside the rebel territory near one of the crossing points.
The government has opened what it says are several safe routes out of eastern Ghouta for civilians, but none are known to have left so far and Damascus and Moscow accuse the rebels of preventing them from fleeing the fighting.
It follows a pause in Syrian government air strikes overnight, with the situation in the besieged enclave on Friday described as "calm".More news: Miami's Mokai Nightclub Loses License After Video Shows Horse Inside Club
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Syrian state TV showed pictures on Friday of what it said was a number of fighters boarding a bus to leave the enclave.
It said the initiative was "based on consultations between Jaish al-Islam and the United Nations, and a number of worldwide actors".
Keen to secure Damascus, government troops and allied militias have been closing in on the enclave since February 18 and have overrun more than half of it.
A clear strategy of the Syrian government's offensive in Eastern Ghouta has been to divide the enclave into isolated sections and so cut off rebel support and supply networks, the BBC's Arab Affairs editor Sebastian Usher says - and now the government appears to have all but achieved that goal.
Numerous rounds of UN-backed peace talks have failed to bring an end to the conflict, and a nationwide ceasefire called for by the UN Security Council last month has not been implemented.
"The regime has cut Ghouta into three parts by cutting the main roads linking them", said the Observatory's chief Rami Abdurrahman.
Some 400,000 people are still thought to live in the area, seven years into Syria's civil war. The Russian military has repeatedly said that terrorists use civilians as human shields and their homes as shelters. Kurdish fighters insist the Turkish military has not yet besieged Afrin.