"So far there are 82 fatalities and more than 160 wounded in a terrorist attack that targeted students on their first day of exams at the University of Aleppo," Governor Mohammed Wahid Akkad told AFP by telephone.
The Britain-based Syrian Observatory for Human Rights said 83 people had been killed in the blasts and at least 150 others wounded, some critically.
State news agency SANA said "it was the first day of exams. Students and displaced people were among the victims," adding that exams have been postponed in light of the attack.
The education minister called for a nationwide "day of mourning" on Wednesday and said President Bashar al-Assad ordered the "immediate rebuilding of damaged parts of the university," state television reported.
As well as students, the university campus houses some 30,000 people who have fled homes in areas of the city ravaged by fighting since rebels seized many neighbourhoods last July.
Video footage posted by students on the Internet showed tearful survivors taking refuge in a campus building.
The explosions struck an area near the university dormitories and the architecture faculty, the Observatory said.
State television said "terrorists launched two rockets" at the campus.
The Observatory said "the nature of the explosions is still unclear. There are conflicting reports of air raids and two explosions on the ground."
The Britain-based watchdog said at least 152 people were killed nationwide, 128 of them civilians.
The violence came as Russia rejected as "counterproductive" Swiss-led efforts at the UN Security Council to seek prosecution of key figures in Assad's regime before the the International Criminal Court.
"We view this initiative as untimely and counterproductive to solving today's main goal -- an immediate end to the bloodshed in Syria," the Russian foreign ministry said.
Only the Security Council has the right to refer the Syria case to the Hague-based court because Syria is not an ICC member.
But Russia -- a traditional Syrian ally that has vetoed three prior council resolutions sanctioning Assad -- argued that a war crimes referral could only escalate the crisis.
"We are convinced that speculation on the subject of international criminal prosecution and a search for the guilty will only entrench the two sides' irreconcilable positions and complicate a search for a political settlement of the Syrian conflict," the Russian statement said.
Moscow also once again reaffirmed its support for a Syrian transition plan agreed by world powers in June that was never implemented because of the fighting.
That deal called for the quick creation of an interim government with full powers, but it never assigned a clear role for Assad and was interpreted differently by Russia and the West.
Syrian Prime Minister Wael al-Halaqi arrived in Tehran on Tuesday for consultations with Damascus's key regional ally, state television reported.
The Fars news agency said the two sides would discuss "Assad's three-step plan" for the political future, which he presented on January 6.
Assad's plan was rejected by the opposition and Western governments as being detached from reality. The plan offered dialogue but only with opposition groups he deemed acceptable, not "terrorists" led by foreigners.
Iran has supplied financial aid to Syria and has admitted to sending military advisers to assist in the regime's nearly 22-month crackdown.
According to UN figures, more than 60,000 people have been killed in the violence in Syria since March 2011.