An internationally brokered ceasefire zone covering parts of Eastern Ghouta went into effect on Saturday.
The Syrian Observatory for Human Rights said the overnight fighting was the first in the enclave since the truce began.
Government troops clashed with fighters of the Faylaq al-Rahman rebel group in the Ain Tarma district, the Britain- based monitoring group said.
The fighting subsided by Wednesday morning but government warplanes then carried out strikes in the area.
Faylaq al-Rahman is allied with former Al-Qaeda affiliate Fateh al-Sham Front and the pro-government Al-Watan newspaper reported on Monday that it was excluded from the truce.
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The new strikes came after two days of government air raids on the town of Arbeen in Eastern Ghouta, which killed 12 civilians, among them children.
The so-called "de-escalation" zone deal, hammered out by government allies Russia and Iran and rebel backer Turkey in May, covers only part of Eastern Ghouta, a large region that is key opposition territory.
A map displayed at a Russian defence ministry briefing appeared to show that the areas hit late on Tuesday and today were inside the ceasefire zone.
On Tuesday, a Russian military official denied that any air strikes had hit inside the ceasefire zone, which is being monitored in part by Russian police.
The Russian defence ministry map appears to show at least part of Arbin may be excluded from the truce zone.
Eastern Ghouta is the second of four proposed ceasefire zones to be implemented, after parts of the southern provinces of Daraa, Sweida and Quneitra.