Syrian army tanks around Aleppo have begun moving in on south-western districts of the city, activists say.
They say the bombardment of rebel-held areas intensified in the early morning, with military aircraft overflying the city at low altitudes.
The BBC's Ian Pannell, in Aleppo, says many casualties have been reported and families are fleeing.
Western nations have warned of a potential massacre in Aleppo, Syria's most populous city.
Syrian state television said that rebels, having failed in Damascus, were now trying to turn Aleppo into a den for their terrorism.
Appeal to medics
The rebels say they have destroyed a number of tanks, but their claim cannot be independently verified.
Our correspondent says the rebels are vastly outgunned and outmanned by forces loyal to Syrian President Bashar al-Assad.
Activists have reported violent clashes around the Salah al-Din and Hamdanieh quarters near the centre of Aleppo.
An emergency call has gone out to doctors to come to Salah al-Din and help if they can, our correspondent says.
On Friday, the Red Crescent suspended some of its operations in Aleppo because of the heavy fighting.
Rebels had been stockpiling ammunition and medical supplies in preparation for the expected assault.
The fighting comes after two weeks during which rebels made significant gains.
On 18 July, an attack at Syrian security headquarters in Damascus killed four senior officials, including the defence minister and President Bashar al-Assad's brother-in-law.
The Free Syrian Army (FSA) took control of several parts of Damascus before being driven out by a government counter-offensive.
The rebels also seized several border crossings with Turkey and Iraq.
There has been fighting around Aleppo for the past week, with the government deploying fighter jets and helicopter gunships to beat back the rebels.
Until recently, Aleppo and Damascus had been relatively free of the violence that has wracked other parts of the country.
Earlier this week, thousands of government forces were moved from the border with Turkey to join fierce fighting in Aleppo, activists said.
On Friday, UN Secretary General Ban Ki-moon urged the Syrian government to halt its offensive and demanded a clear statement that chemical weapons would not be used under any circumstances.
Syria has implicitly acknowledged that it has chemical weapons but says it will not use them against its own people, only against foreign invaders.
The former head of the UN monitoring mission in Syria, Maj Gen Robert Mood, said it was "only a matter of time" until President Assad was ousted.
On Sunday, the Syrian Observatory for Human Rights reported that at least 19,106 people had been killed since March 2011. The UN said in May that at least 10,000 people had been killed.
Syria blames the violence on foreign-backed "armed terrorist gangs".
In June, the Syrian government reported that 6,947 Syrians had died, including at least 3,211 civilians and 2,566 security forces personnel.