The rebels also took over a third border crossing -- and the second one along Syria's frontier with Iraq -- another sign the regime's tight grip on the country is wobbling.
The fighting in Aleppo comes on the heels of intense clashes in the capital, Damascus, as rebel forces target the pillars of regime power in their attempts to usher in what they hope will be the end of Assad's rule.
"There were huge explosions and the gunfire didn't stop for several hours," said Aleppo-based activist Mohammad Saeed. "The uprising has finally reached Aleppo."
The city has remained largely loyal to Assad and been spared the kind of daily bloodshed that has plagued other areas.
But Saeed said dozens of fighters from the rag-tag Free Syrian Army entered Aleppo -- a commercial hub -- from the countryside and were fighting regime troops from inside.
It was the first sustained fighting in the city center, focused on the Salaheddine district, although there have been protests in Aleppo and violence on the outskirts.
The rebels have put the regime on the defensive after a week of battles in the capital, Damascus, including a bombing that struck at the heart of the regime, killing four high-level government officials. The coming days will be crucial to determining whether the regime can recover from the blows, which have punctured the sense that Assad's hold on the country is impenetrable.
Rebels also took over the Syrian side of the border crossing at the Iraqi town of Rabiya, 320 miles northwest of Baghdad, according to Atheel al-Nujaifi, the governor of Iraq's Ninevah province.
Iraqi officials said rebels tore up and shot at posters of Assad but did not face any resistance from regime authorities who surrendered the sprawling, dusty border crossing peacefully. Iraqi officials quickly barricaded the crossing and ordered additional troops to secure the area.
Rebels also seized the Syrian side of the border crossing at the Iraqi border town of Qaim on Thursday. Rebels also attacked a remote Syrian military post near the border on Thursday, killing 21 soldiers, and overran a border checkpoint with Turkey last week.
French Foreign Minister Laurent Fabius warned Assad to prepare to leave.
"Bashar Assad's regime is condemned by his own people, who show great courage," Fabius said. "It's time to prepare for the transition and the day after."
He also encouraged the opposition -- which is fractious and beset by infighting -- to unite.
"It's time for the opposition to get started on taking control of the country," he said. "We want the rapid formation of an interim government that will be representative of the diversity of Syrian society."
Damascus and Aleppo are both home to elites who have benefited from close ties to Assad's regime, as well as merchant classes and minority groups who worry their status will suffer if Assad falls.
But for months, rebels have been gaining strength in poorer towns and cities in the Aleppo countryside, gaining footholds near the Turkish border.
Anger has been building inside Aleppo at the government's deadly crackdown on the uprising and in recent months, huge anti-government demonstrations have broken out, particularly among students at Aleppo University.
In May, Syrian forces stormed student dormitories during an anti-government protest at the university, firing tear gas and bullets in an hours-long siege that killed four students and forced the closure of the state-run school.
An amateur video posted online by activists showed Aleppo residents walking with bags of belongings or packing into cars and driving away.
Another video showed protesters pounding an iron bust of Assad's late father, Hafez, with rocks in an attempt to break it.
Activists and residents reported relative calm in Damascus on Saturday, although sporadic gunfire and explosions could be heard.
Two residents who did not want to be identified for safety reasons said by telephone that the fighting peaked between 1 a.m. and 3 a.m. local time.
One of the residents said most shops in the capital were closed Saturday and traffic was light.
Authorities have set up checkpoints at the entrances of Damascus in an effort to separate it from rebellious suburbs, and the resident said many grocery stores and vegetable vendors were unable to get supplies.
Piles of rubbish were starting to pile up in many parts of the city.
"The tension is palpable, people are scared about what might be coming," the resident said by telephone from the upscale middle class Mazzeh district. "A lot of people are just staying at home."
The Britain-based Syrian Observatory for Human Rights and a Damascus-based activist said two people were found dead in the Midan district after regime forces stormed their apartment. The activist, who gave his name as Omar al-Dimashqi, said the pair had been stabbed with knives.
Syrian forces recaptured the battle-scarred neighborhood on Friday and proudly showed reporters the dead bodies of rebel fighters lying in rubble-strewn streets.
The fighting in Damascus has sent thousands of Syrians pouring into neighboring Lebanon and Iraq.
Iraqi officials said about 1,000 nationals had left in eight flights from Damascus over the last two days to escape the escalating civil war. An estimated 5,000 more had poured through a land crossing by Saturday, despite the rebel takeover of a major Syria border post farther north.
Capt. Saad al-Khafaji of the state-owned Iraqi Airways said Iraqi authorities sent four airplanes to Damascus airport Saturday to evacuate Iraqis stranded in the Syrian capital.
Also Saturday, U.N. Secretary-General Ban Ki-moon said he is sending U.N. peacekeeping chief Herve Ladsous to Syria to assess the situation.
The U.N. Security Council unanimously approved a resolution Friday renewing the 300-strong U.N. observer force in Syria for 30 days.
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