Syrian government forces and rebels engaged Saturday in fierce clashes throughout the vital and culturally rich city of Aleppo, with portions of a storied marketplace going up in flames.

Abu Abdallah, an opposition activist in Aleppo, told CNN that rebel forces had liberated at least four neighborhoods by the third day of an offensive against President Bashar al-Assad's forces.

But the government trumpeted its actions against the opposition.

"The armed forces on Saturday continued to target hideouts and gatherings of terrorists in Aleppo city and its countryside, killing and injuring dozens of terrorists and destroying their vehicles," according to the state-run Syrian Arab News Agency (SANA).

The see-saw fight for Aleppo, once considered an al-Assad stronghold, has continued nearly unabated since July, though the number of casualties has steadily increased.

Syrian forces targeted "terrorists" at several sites, including part of the city's medieval souk, a historic market, and killed and wounded several of them, SANA reported.

Video posted on YouTube showed a fire that had been initially set off on Saturday night continued to spread through the souk Sunday amid the sound of gunfire. The description on the video said it was recorded Saturday after "Assad gangs" burned the market.

CNN is unable to independently verify the veracity of the video.

The marketplace, once popular with tourists, is a labyrinth of covered alleys.

The opposition Local Coordination Committees of Syria said, "the (rebel) Free Syrian Army and the families of the city were unable to extinguish the fire due to the spread of regime snipers."

Aleppo is a UNESCO World Heritage Site, dominated by an ancient citadel. The city also is a center for the art and was named Islamic capital of culture six years ago.

"No part of the ancient treasure of humanity shall be destroyed," Sok An, chair of the group's world heritage committee, said in August. "It is the collective responsibility of all humanity to urgently ensure the safeguarding and protection of Aleppo's cultural properties."

Opposition groups reported clashes near al-Nayrab Military Airport in the south of the city, where initial information indicate that the rebels damaged at least two helicopters and a main runway after firing mortars. Several districts of the city came under artillery shelling, the opposition said.

Government forces hammered rebels in several locations, inflicting substantial casualties, according to SANA. It said troops assumed control of the al-Amiriyeh area and much of Tal al-Zarazir in Aleppo.

Al-Assad has severely limited the access of international journalists to the country, so CNN is unable to verify opposition and government claims of violence.

At least 126 people were killed in fighting across the country Saturday, according to the LCC. Among those killed were 64 people in Damascus and its suburbs.

In the Damascus neighborhood of Barzeh, 43 people were killed over three days after government forces came through. The LCC linked to an online video, purportedly shot in Barzeh on Saturday, showing columns of armed, camouflaged soldiers walking down a busy street as two tanks rolled by.

SANA reported a military unit killed "many terrorists" in Barzeh.

Neighborhood residents in Homs held a friendship march Saturday, according to SANA. Homs Gov. Ahmad Munir Mohammad said, "no matter how hard the enemies try, the Syrian people will remain strong and steadfast in the face of the conspiracies."

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