The Syrian army has intensified its operations in the central part of rebel-held eastern Ghouta, an area where it is close to cutting the enclave in two.
State television reported on Saturday that the army was advancing near Mesraba and Mudeira, two small towns which represent the last link between the northern and southern halves of the enclave, near the Syrian capital Damascus.
Jaish al-Islam and Failaq al-Rahman, the two main insurgent groups in eastern Ghouta, say they have staged counter-attacks in recent days that retook some lost positions.
The ferocious three-week assault on the last major rebel stronghold near Damascus has captured about half its area and killed 960 people, according to a war monitor.
The Britain-based Syrian Observatory for Human Rights also said on Saturday that warplanes, helicopters and artillery were used in bombardment of the area overnight.
Syrian President Bashar al-Assad and Russia, his main ally, say the campaign is needed to end rebel shelling of Damascus and to end the rule of Islamist insurgents over the area's civilians.
The offensive follows the pattern of previous assaults on rebel strongholds, deploying massive air power and tight sieges to force insurgents to accept "evacuation" deals.
These involve rebels surrendering territory in exchange for safe passage to opposition areas in northwest Syria, along with their families and other civilians who do not want to come back under Assad's rule.
Late on Friday, a small number of fighters and their families from the former al-Qaeda affiliate previously known as the Nusra Front left eastern Ghouta under such a deal.
But the group represents only a small portion of the insurgent presence in the enclave, and both Jaish al-Islam and Failaq al-Rahman have said they are not negotiating a similar deal for themselves.
The intensity of the government's attack on an enclave that has been besieged since 2013 and suffers acute shortages of food and medical supplies has drawn Western condemnation and demands by UN aid agencies for a humanitarian halt in fighting.
The United Nations estimates that some 400,000 people are trapped in the enclave.