The battles in Aleppo followed a day of heavy fighting and came after the regime rushed reinforcements to the northern city, where rebels launched an all-out assault for control of the country's commercial hub on July 20.
"There are clashes in the Muhafaza district and shelling on the Mushhad and Sheikh Badr neighbourhoods, which killed a child and injured seven people," the Britain-based Syrian Observatory for Human Rights said.
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The Salaheddin neighbourhood, scene of fierce fighting for days, was also bombarded by troops during the night, the group said.
An AFP correspondent witnessed rebels of the Free Syrian Army overrunning a police station Aleppo's Shaar district on Wednesday.
He said at least two policemen were killed, an unknown number wounded and several captured in the clashes that left the station's walls riddled with bullets.
The building was later set alight.
The Observatory reported 19 civilians and three rebels killed in Aleppo fighting on Wednesday but did not give a separate toll for soldiers.
Syrian newspaper Al-Watan, which is close to the regime, led Thursday with the headline "Aleppo, the mother of all battles," adding that "the army continues to chase terrorists in the outskirts of Damascus and the province."
"For several days, Aleppo has been the scene of violent clashes between the Syrian army and terrorist groups equipped with modern Turkish and European weapons who are trying to take control of Aleppo," the newspaper said.
"In recent hours, the army was able to expel these terrorists, who are trying to take the outskirts of Aleppo, but the battle will continue for some time," the newspaper continued.
"According to Western diplomats, there are 12,000 terrorists, most of them from Libya, Tunisia, Egypt, Afghanistan and a very small number of Syrians."
Citing an Arab diplomatic source, the newspaper added: "Aleppo will be the last battle waged by the Syrian army to crush the terrorists and after that Syrian will emerge from the crisis."
Despite the continued fighting in Aleppo, there were "mass demonstrations in the Furqan, Ashrafiyeh and New Aleppo districts calling for the fall of the regime and the departure of President Bashar al-Assad," the Observatory said.
In southern Damascus, street battles were being fought on Thursday in the Yarmouk Palestinian refugee camp, the Observatory said.
"There are clashes on Street 30 in the Yarmouk camp between Syrian regime forces and fighters from rebel units. Explosions can be heard," it said.
A resident of the camp reached by phone confirmed the fighting.
"It started at 7:00 am. The night was quiet. They are using RPGs and heavy machineguns," he told AFP.
Elsewhere in the city, an activist in the southern neighbourhood of Tadamun, who gave his name as Abu Qais al-Shami, said several districts in the southern part of the city were under assault on Thursday by regime forces.
"Last night was quiet but people woke up to the sound of explosions and shelling from seven o'clock in the morning," he told AFP.
Another Damascus resident reached by phone told AFP heavy clashes were ongoing in the southern Al-Hajar Al-Aswad district, where the regime was using helicopter gunships.
Nationwide, at least 143 people were killed on Wednesday, according to Observatory figures, including 75 civilians, 41 soldiers and 27 rebel fighters.
