They called on residents of government-held areas in western Aleppo to stay at home or in underground shelters as they spread their offensive, saying they were coming to "liberate" their land.
Separately, the Iranian and Syrian foreign ministers were meeting in Moscow with their Russian counterpart to discuss the war. The Syrian military said the rockets were Russian-made Grad missiles.
Monday's attack began with rebels detonating three vehicle-borne explosives against government positions to the city's south-west and attacking with hundreds of rockets, the Britain-based Syrian Observatory for Human Rights said.
At least 21 people have been killed since Friday, including a woman and two children, as a result of rebel attacks, SOHR reported.
A Russian fighter jet flew dangerously close to a US fighter jet over eastern Syria, US defence officials said on Friday, highlighting the risks of a serious mishap in the increasingly crowded airspace.
Ibrahim al-Haj, a member of the first responders team the Syrian Civil Defense that operates in rebel-held Aleppo, said airstrikes Sunday on districts near the front line caused material damage.
Syria Kurds announce start of campaign to retake Raqqa
The SDF is dominated by YPG militia, which Ankara says is an affiliate of the outlawed Kurdistan Workers' Party (PKK). Raqqa became the scene of some of IS's worst atrocities, from stonings and beheadings to the trading of sex slaves.
The Syrian army said troops were repelling the attack on Zahraa. "Fighting is still ongoing but the intensity has dropped".
U.N. Special Envoy Staffan De Mistura has estimated 8,000 of them are rebel fighters, and no more than 900 of them affiliated with Fatah al-Sham.
Syrian state media says that rebels fired shells containing toxic gas into government-held parts of Aleppo, leaving dozens of people including civilians in need of treatment.
The government has maintained a siege on the rebel-held eastern quarters since September. "It may go beyond lifting the siege to liberating the whole city".
Fatah al-Sham claimed credit for two vehicle bombs, saying in a statement that a "martyrdom-seeking fighter" drove a tank laden with explosives and parked it, before it was detonated and the fighter "returned to his brothers".
Sakkar, said "all the revolutionary factions, without exception, are participating in the battle".
Pence, Kaine plan campaign rallies in Northern Virginia
The visit also gives Trump access to the crucial voters of western Wisconsin, a swing state in almost every poll . He says the Republican nominee is "a man I've prayed with and gotten to know on a personal level".
The head of the political office of the Aleppo-based rebel group Fastaqim denied the reports.
Despite Russian air support, the Syrian regime has had limited success in its attempts to seize the whole of Aleppo.
The allegation came on the third day of a rebel offensive to break a three-month siege of the opposition-held east of Aleppo.
About 1,500 rebels have massed on a 15-km front along the western edges of Aleppo since Friday, scoring quick gains in the Dahiyet al-Assad district, but struggling to push east since then.
Heavy rain put out the fires but also hampered Syrian air operations, creating what one rebel dubbed "a divine no-fly zone".
But Kremlin spokesman Dmitry Peskov said Putin "considers it inappropriate at the current moment", adding the president thought it necessary to "continue the humanitarian pause" in the war-ravaged city.
Bilic frustrated by crowd trouble as London Stadium 'felt like home'
A Chelsea fan said he and his eight-year-old daughter were pelted with coins during the disorder. We will stay humble because we want to continue winning.