(CNN) -- 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."
U.S. to Iran: Stop shipping arms to Syria
The United States warned Iran to stop providing arms to al-Assad even as it announced millions of dollars in non-lethal support for the opposition attempting to oust the government.
Secretary of State Hillary Clinton called on Syria's neighbors to take steps to prevent Iran from using their land and airspace to transport weapons to al-Assad's forces.
Clinton's warning followed an admission, according to Iranian state-run media reports, by the commander of Iran's Revolutionary Guard that its elite Quds Force was operating inside Syria but not involved directly in military action.
Clinton announced the United States is donating $15 million to unarmed Syrian opposition groups, bringing the total U.S. aid for the opposition to nearly $45 million.
The latest donation "translates into more than 1,100 sets of communications equipment, including satellite-linked computers, telephones, and cameras, as well as training for more than 1,000 activists, students, and independent journalists," she said.
The United States also is donating an additional $30 million in humanitarian assistance, primarily in the form of food, water and medical supplies, Clinton said.
Syria's chemical weapons a target?
A former senior officer in the Syrian Army said Friday that Iranian technicians are helping with the Syrian government's research into chemical weapons.
Adnan Sillu, a former major general who says he was chief of staff of chemical warfare, also said Syria can easily transfer the weapons to Hezbollah, the Lebanese militia organization that fought a border conflict with Israel in 2006.
Syrian opposition posted a series of videos on YouTube suggesting rebels are beginning to focus on where al-Assad's government stores its chemical weapons.
The videos were first uploaded in July. Narrators using Google Earth satellite imagery describe in detail several sites where they allege that chemical weapons and missiles are stored or manufactured.
There is no way for CNN to independently verify what the videos purport to show.
Sillu said moving the weapons would be easy for the government should they be at risk of falling into the rebels' hands.
His comments follow word from U.S. Secretary of Defense Leon Panetta that the Syrian government has moved chemical weapons at various sites for security reasons.
U.S. officials have said they believe that the stashes remain secured by the Syrian military.
Background on the conflict
The Syrian conflict broke out in March 2011 after unarmed protesters, inspired by the success of popular uprisings in Egypt and Tunisia, took to the streets demanding political reform and an end to four decades of rule by the Assad family.
The movement quickly devolved into an armed conflict after a brutal and continuing crackdown by government forces.
Since the unrest began, more than 30,000 people have been killed, the opposition Syrian Observatory for Human Rights said.
CNN's Amir Ahmed, Mohammed Jamjoom, Barbara Starr and Hamdi Alkhshali contributed to this report.