A fourth explosion a few hundred meters (yards) away also struck near the edge of the Old City, a world heritage site, where rebels and government forces have been battling in fierce street fighting.
Long free of the violence that has engulfed much of the rest of the country, Aleppo in the past two months has become a key battleground between regime forces and rebels trying to oust President Bashar Assad. The opposition launched an initial offensive on the city, Syria's largest and commercial hub, in July, which has left large swaths of the ancient city shattered.
Rebels last week announced a new concerted push to capture Aleppo, which would be a major strategic prize, giving the victor new momentum. It would also provide the opposition with a base, with easy logistical supply lines with Turkey to the north, from which to carry out their fight against the regime in the rest of the country.
Syria's state-run SANA news agency said the bombings early Wednesday, which targeted Saadallah al-Jabri square, were carried out by "terrorists" and killed at least 33 people and wounded dozens more. Authorities refer to rebels fighting to topple Assad as terrorists and armed gangs.
There was no immediate claim of responsibility for the attacks. Previous bombings in Aleppo and Damascus have raised concerns that the al-Qaida terror network is becoming increasingly active in Syria. Jabhat al-Nusra, or Victory Front, a Sunni extremist group in Syria, claimed responsibility for many of them.
Footage broadcast on the state-run Ikhbariya channel showed massive damage around the square, which also houses a famous hotel and a coffee shop that had been popular with regime forces. One building appeared leveled to the ground. The facade of another was heavily damaged.
The station showed video of several bodies, including one being pulled from the rubble of a collapsed building. Rescue workers stood atop piles of concrete and debris, frantically trying to pull out survivors.
"It was like a series of earthquakes," said a shaken resident who declined to be identified for fear of reprisals. "It was terrifying, terrifying."
Speaking to the AP by telephone, the resident said the officers' club and the hotel were almost completely destroyed. His account could not be immediately verified, although the TV footage showed at least one building reduced to rubble.
Activists could not reach the area, which is controlled by security forces and sealed off with checkpoints.
A Syrian government official said the number of deaths would likely increase because many of the wounded were in critical condition. Regime troops killed two more would-be suicide bombers before they could detonate their explosives, he said on condition of anonymity in line with government regulations.
Syrian state TV showed the bodies of three men wearing army uniforms at the site of the explosions. One of them appeared to be wearing an explosive belt with a timer tied to his wrist.
Aleppo-based activist Mohammad Saeed said the explosions went off minutes apart at one of the city's main squares. He said the blasts appeared to have been caused by car bombs and were followed by clashes and heavy gunfire.
"The area is heavily fortified by security and the presence of shabiha," he said, referring to pro-regime gunmen. "It makes you wonder how car bombs could reach there."
Activists and Syrian state media said a fourth car bomb went off in the Bab Jnein area near the Old City where the Chamber of Commerce is located. It was not immediately clear how many casualties there were from that blast.
The Britain-based Syrian Observatory for Human Rights, which relies on a network of activists on the ground, said at least 40 people were killed and around 90 wounded in the four blasts, most of them members of the regime forces.
It said mortars also targeted the nearby political security department around the same time of the bombings.
The Syrian security official, however, said most of Wednesday's casualties were civilians.
"We condemn these crimes and this terrorist explosion and we also condemn the countries that conspire against Syria and stand behind the terrorists," said the speaker of the Syrian parliament, Mohammad Jihad al-Lahham, told the assembly Wednesday.
During the course of the 18-month-uprising against Assad, suicide and car bombings targeting security agencies and soldiers have become common in Syria, particularly in the capital, Damascus.
But Aleppo has been spared from such bombings and from the mayhem that struck other Syrian cities, particularly in the first year of the revolt. Then, in February, two suicide car bombers hit security compounds in Aleppo's industrial center, killing 28 people.
The uprising against Assad erupted in March 2011 and gradually morphed into a bloody civil war. The conflict has killed more than 30,000 people, activists say, and has devastated entire neighborhoods in Syria's main cities, including Aleppo.
The city, one of the world's oldest continuously inhabited cities, has been the site of fierce battles for more than two months between regime troops and rebels fighters that have brought relentless shelling and gun battles.
Over the weekend, a fire sparked by fighting tore through the city's centuries-old covered market in the Old City, burning over 500 shops. At 12 kilometers (7.5 miles), it is the Middle East's longest souk and is part of Aleppo's old center that was added in 1986 to UNESCO's list of World Heritage sites.