Syrian forces have kept up a day-long ground and air attack against rebels in parts of the city of Aleppo.The BBC's Ian Pannell, who is in Aleppo, has seen skirmishes, with a number of rebel fighters killed.
Rebels with the Free Syrian Army (FSA) say they have repelled an army incursion and destroyed tanks, but there is no independent verification.
Western nations have warned of a potential massacre in Aleppo, Syria's most populous city.
There are also reports of fighting in the western city of Homs, where state media said a number of rebels had been killed, and in the provinces of Hama and Deraa.
Activists said Syrian tanks began moving in on south-western districts of Aleppo city early on Saturday.
They said the bombardment of rebel-held areas intensified with military aircraft overflying the city at low altitudes.Our correspondent says there has been constant shelling and mortar rounds all day, with troops firing from helicopters. Many casualties have been reported and a steady stream of vehicles has been heading out of the city carrying hundreds of families trying to escape the violence and deteriorating conditions.
The rebels in Aleppo are vastly outgunned and outmanned by forces loyal to Syrian President Bashar al-Assad, he adds.
Activists have reported violent clashes around the Salah al-Din and Hamdanieh quarters near the city's centre.
A government official told the AFP news agency: "Rebels are stationed in narrow streets, in which fighting will be difficult."
An emergency call has gone out to doctors to come to Salah al-Din and help if they can, our correspondent says.
Rebels had been stockpiling ammunition and medical supplies in preparation for the expected assault.
On Friday, the Red Crescent suspended some of its operations in Aleppo because of the heavy fighting.
Both sides are braced for heavy casualties.
The Syrian Observatory for Human Rights said 29 people were killed in Aleppo on Saturday. They were among at least 90 people to die across the country throughout the day.
Rebel gains Syrian state television said that rebels, having failed in Damascus, were now trying to turn Aleppo into a den for their terrorism.
Russia, an ally of Syria, warned of a "tragedy" in Aleppo, saying international support for the rebels would lead to "more blood".
Russian Foreign Minister Sergei Lavrov said the Syrian government should take the first steps but could not be expected to "stand by" when rebels were occupying Aleppo and other areas.
He said Western nations and Syria's neighbours, which have pushed for international action to stop the violence, were "essentially encouraging, supporting and directing an armed struggle against the regime".
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.
Chemical fears Until recently, Aleppo and Damascus had been relatively free of the violence that has wracked other parts of the country.
But there has been fighting around Aleppo for the past week, with the government deploying fighter jets and helicopter gunships.
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 Saturday, the Syrian Observatory said that more than 20,000 people, including civilians, rebels, government soldiers and government figures, since the uprising began in March last year.
The UN said in May that at least 10,000 people had been killed.
In June, the Syrian government, which blames the violence on foreign-backed "armed terrorist gangs", reported that 6,947 Syrians had died, including at least 3,211 civilians and 2,566 security forces personnel.