Saturday's fighting was centered around the southwestern neighborhood of Salaheddine, one of the first areas seized by the rebels since they began a push to control the city after being routed from the capital, Damascus.
Activists said helicopters were strafing the area and rebels faced artillery barrages and regime tanks trying to push into the neighborhood.
An Aleppo-based activist, Mohammed Saeed, said the government counterattack had begun and rebels were fighting back in several other areas as well.
"Thanks be to God, they haven't succeeded in entering any of the (rebel-held) neighborhoods yet," he said.
President Bashar Assad's forces have been massing outside the city over the past few days, and Saeed said rebels from around the country also have been pouring in to help defend the areas under their control.
"About 1,000 fighters have come from the Free Syrian Army from outside the province of Aleppo to help," he said, referring to the main rebel group.
State television, in a rare comment on the situation in Aleppo, reported that government forces had inflicted heavy losses on groups of terrorists, the term the regime uses for the rebels.
The pro-government daily newspaper Al-Watan called it "the mother of all battles" in a banner headline Saturday.
The Britain-based Syrian Observatory for Human Rights said the government attack started before dawn with the sustained bombardment of several areas, followed by the movement of armored vehicles backed by attack helicopters.
Based on reports from its network on the ground, the Observatory reported attacks in the northeastern neighborhood of Sakhour as well as other areas, and said the rebels had disabled a number of regime armored vehicles.
The group estimated that 22 people, most civilians, have been killed in Saturday's fighting. The estimated toll for the past week in Aleppo is 162, a figure that does not include government soldiers killed.
The international community has expressed growing concern that there could be major bloodshed if Syrian troops retake Aleppo. But Western nations and their allies have found themselves powerless to prevent the situation from deteriorating despite a series of diplomatic efforts, including a cease-fire agreement that never took effect.
"The regime's destruction of its own city shows the level of oppression that has been reached in Syria," said Turkish Foreign Minister Ahmed Davutoglu from the central city of Konya. "We will do our best to stop this oppression."
Russian Foreign Minister Sergey Lavrov, however, stood by the regime.
"Now the city of Aleppo is occupied by the armed opposition; another tragedy is imminent there," he said. "How can it be hoped that in such a situation the government will simply give in, say 'Okay, I wasn't right, overthrow me, change the regime it's simply unrealistic."
Russia has been a key source of support for Syria, although Moscow officials in recent months have said they are simply taking a more even-handed approach while the West offers blind support to the rebels.
It has been a difficult two weeks for the Syrian government with rebel assaults first on the capital, Damascus, then on Aleppo, as well as several high-profile defections and a bomb that killed four top security officials.
The regime, however, launched a swift counteroffensive and quashed the assault on the capital with a combination of heavy weapons and house-to-house searches. Scores of people were killed. Opposition activists said they expected similar tactics in the coming days to keep Aleppo from falling into rebel hands.
The rebels are outgunned by the Syrian forces, making it difficult for them to hold any territory for long. But the rebels' run on Damascus and Aleppo suggests they could be gaining in power and organization.
With a population of about 3 million, Aleppo is Syria's commercial hub, a key pillar of support for Assad's regime.
If the rebels in Aleppo really try to make a stand against the regime, however, they risk being annihilated by superior firepower and may yet decide to withdraw to preserve their forces as what happened in Damascus last week.
Saudi Arabia and other nations have spoken positively of arming the rebels, though no country is known to be doing so.
Saudi King Abdullah announced a national campaign to collect money for "our brothers in Syria" on July 22, and on Saturday the country's press agency said Saudi donations had reached more than $72 million.
Italy also welcomed Friday's release of two Italian electrical engineers, who had been captured eight days ago by militants.
Italian company Ansaldo Energia, which supplies and installs power generation plants, confirmed that the two men Domenico Tedeschi and Oriano Cantani worked for a subcontractor in Syria.
Tedeschi told reporters in Damascus that they had been kidnapped by five or six masked men, who intercepted their car as they drove to the airport.
He said the men were robbed, then kept at a small villa. "The Syrian army found us at midday on Friday and they organized everything to release us safe," he said.
Associated Press writers Albert Aji in Damascus, Colleen Barry in Rome and Jim Heintz in Moscow contributed to this report.