Rebel rocket fire killed 13 people in the northern city of Aleppo on Friday, as troops launched an offensive on rebels in Daraa province of southern Syria, state media said.
The Syrian Observatory for Human Rights also reported the bloodshed in Aleppo and said a large-scale army operation was underway in Daraa for control of hills held by rebels.
The Britain-based monitoring group said five rebel fighters and an unspecified number of soldiers were killed in Daraa, where clashes raged into the evening.
State television said rocket fire by rebels on the government-held Ashrafiyeh district of Aleppo killed 13 people, including women and children, and wounded 17.
The Observatory said at least 16 people were killed, including six children, and 60 wounded in the Aleppo rocket attack by Islamist rebels.
Aleppo has been split into areas held by the regime and opposition since shortly after fighting broke out in Syria's former economic hub in 2012.
Regime warplanes have waged an aerial offensive on the eastern, rebel-held districts, frequently dropping barrel bombs on the area.
And opposition forces have regularly fired rockets into government-held areas, as rival forces clash on the ground.
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Water supplies to the city were cut for a week by rebel groups, including Al-Qaeda's Syrian branch, Al-Nusra Front.
But the Red Crescent said Thursday that some supplies had been restored.
Also on Friday, government troops "carried out a wide-scale operation in the (Daraa) town of Nawa against terrorist groups" and rebel-held hills, state news agency SANA said.
The Observatory said regime warplanes carried out at least 15 raids in and around Nawa as ground forces battled the rebels.
The hills connect rebel positions in Daraa and Quneitra, near the frontier with Israel.
The Syrian Revolution General Commission, a network of activists on the ground, said dozens of rockets were fired on Nawa "within a short time".
Daraa is where the uprising against President Bashar al-Assad's regime first broke out in March 2011.
Rebels say they have united tens of thousands of fighters in a so-called Southern Front set up earlier this year.
Fierce battles in April for control of the Nawa hills killed 90 soldiers and rebels, according to the Observatory, which takes its information from a vast network of medics and opposition activists.
Elsewhere, the Observatory said a car bomb exploded Friday near a building in Shyl village in the eastern province of Deir Ezzor, killing seven rebels and three children.