Jaafari said the blasts, which occurred as students at the university were taking exams, were a terrorist attack, The New York Times reported.
Syrian officials were not immediately sure of the explosions' origins, but the Times said they may have been caused by bombs or missiles fired from aircraft. The university -- in a part of Aleppo controlled by forces loyal to President Bashar Assad -- issued a statement calling the attacks a "criminal act" and blaming them on the Syrian air force.
The university said the attacks destroyed buildings and caused "massive destruction in the surrounding roads."
The attacks appeared to be part of an accelerated battle for control of Syria's largest city, the Times said.
Rebel groups posted photographs and video online showing bodies, burned-out vehicles and property damage at the university, the report said.
Elements of the Free Syrian Army in Damascus were engaged in new fighting in the capital with government forces, following Syrian air force attacks on rebel positions.
Elsewhere, the Syrian Observatory for Human Rights, which operates out of London, said dozens more had been killed and injured as regime forces shelled major cities.
The Syrian Network for Human Rights, another London group, said 202 people died across Syria Tuesday, including 25 children and 16 women. The group, whose figures were not confirmed independently said 94 of the deaths occurred in Aleppo, while 33 were in the greater Damascus area and 29 in Homs.
The rebel Local Coordination Committees of Syria said at least 15 people, including eight children, were killed in Houla by regime shelling, CNN reported. Tanks were shown on video shelling a highway near the town.
Government forces shelled the city of Homs three times, rebels said, killing and injuring dozens of people.
Two Syrian generals captured by rebels pleaded with Assad to secure their release by agreeing to release "50 innocent civilians." They said they were being treated well by members of the rebel Free Syrian Army, but they had not yet received any response from Assad.
In a letter to the U.N. Security Council, the French foreign minister called for aggressive action against Assad and urged the International Criminal Court to try him as a war criminal.
The United Nations says at least 60,000 people have died during the nearly two-year rebellion.