Several Syrian rebel factions, including the Al Qaeda-linked Jabhat al-Nusra, united to launch a new offensive, which they called "If You Return, We Return," near the capital city of Damascus on Tuesday.
Activists and rebels reported that they shot mortars at regime forces that were shelling the suburb of Derayya, according to Reuters.
Meanwhile, the BBC cited Syrian state TV reporting that a car bomb had killed and wounded several people in Damascus.
"Three citizens were martyred and others were injured in terrorist suicide bombing using a car bomb which took place in al-Tadamun neighborhood in Damascus," the state-run Syrian Arab News Agency reported.
The Syrian Observatory for Human Rights, a UK-based rights group that supports the opposition and relies on a network of activists in Syria, said the car bomb killed seven people and wounded 15 more.
Rebel factions have occupied various suburbs outside Damascus, but Syrian President Bashar al-Assad's forces have turned back their attacks. In some cases, the regime has set up blockades cutting off the rebels' supply routes.
An activist in Damascus told Reuters the new offensive was not likely to push back Assad's forces or result in a significant victory.
"The regime's top forces are there," he said. "We on the ground consider these to be 'show' operations from the Free Army, especially in cooperation with Ahrar al-Sham and Nusra. It's a war of attrition. There is no winner and no loser."
More than 100,000 people have been killed in the brutal civil war, and millions of Syrian civilians more have been displaced since the fighting began more than two years ago.