What caused the blasts remained unclear.
Anti-regime activists trying to topple President Bashar Assad's regime said his forces carried out two airstrikes. Syrian state media, for its part, blamed rebels fighting the Syrian government, saying they fired rockets that struck the campus.
Aleppo, Syria's largest city and a commercial capital, has been harshly contested since rebel forces, mostly from rural areas north of the city, pushed in and began clashing with government troops last summer.
Entire neighborhoods have been destroyed since in fighting and frequent shelling and airstrikes by government forces who seek to dislodge the rebels.
The competing narratives of the two blasts at the city's main university highlight the difficulty of confirming reports from inside Syria. The Syrian government bars most media from working in the country, making independent confirmation difficult, and both anti-regime activists and the Syria government sift the information they give the media in an effort to boost their cause.
Aleppo's university is in the city's northwest, a sector controlled by government forces, making it unclear why government jets would target it, as opposition activists claim.
Syria's state news agency blamed the attack on rebels, saying they fired two missiles at the university. It said the strike occurred on the first day of the mid-year exam period and killed students and people who were staying at the university after being displaced by violence elsewhere. The agency did not say how many people were killed and wounded.
The scale of destruction in videos shot at the site, however, suggested more powerful explosives had been used than the rockets the rebels are known to possess.
The Britain-based Syrian Observatory for Human Rights cited students and medical officials as saying that 83 people were killed in the blasts. Several of the more than 150 people injured were in critical condition, it said.
The group, which relies on a network of contacts inside Syria, said it was unclear what caused the blasts.
Syria's crisis began in March 2011 with protests calling for political reform. The conflict has since turned into civil war, with scores of rebel groups fighting Assad's forces throughout the country.
The U.N. says more than 60,000 people have been killed.
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