The UN special envoy for Syria, Staffan de Mistura, says he is "appalled and shocked" that rebels in Aleppo are targeting civilians in the city.
The "relentless and indiscriminate" rocket attacks had killed scores of civilians in western Aleppo in the past 48 hours, Mr de Mistura said.
Such attacks could amount to war crimes, he said.
On Friday, rebels began an offensive aimed at breaking the government siege of east Aleppo.
About 275,000 people have been besieged in the east of the city for months.
Russian and Syrian government planes began bombarding Aleppo in September. More than 2,700 people are said to have been killed and injured since then.
Russia suspended its air campaign on 18 October to allow evacuations of sick and wounded people but few have heeded the call to leave.
On Sunday, state media in Syria said rebels had used chemical weapons against government-controlled districts of Aleppo.
A spokesman for one rebel group denied the claim, saying rebel groups did not possess such weapons, the Associated Press news agency reports.
Sana news agency said 35 people in the districts of Dahiyet al-Assad and Hamdaniya had suffered shortness of breath and numbness.
More than 40 civilians are reported to have been killed in western Aleppo since the rebel attacks began, activists say.
The UK-based Syrian Observatory for Human Rights said 16 were children. It added that 55 soldiers had also died - as well as 64 rebels.
There is no confirmation of these casualties.
Rebels from outside Aleppo are said to be at the forefront of the new offensive, targeting Hamdaniya, which is currently held by troops of Syrian President Bashar al-Assad.
The rebel groups include Jabhat Fateh al-Sham, formerly the al-Qaeda-linked Nusra Front, as well as fellow Islamists Ahrar al-Sham.
It is the rebels' second attempt to break the Aleppo siege. In August they temporarily opened a corridor between the east and west after the government entirely encircled them for the first time in July.
The city, previously Syria's economic hub, has been divided between the two sides since 2012.