The aircraft crashed soon after it took off from an airbase in the capital on a routine training mission. The military said the plane experienced a mechanical failure.
Included in the toll were at least 25 students, a teacher who died from burn injuries she sustained while helping others get out of the burning building and the pilot of the training aircraft.
Bangladesh declared Tuesday a day of national mourning, with the flags flying at half-mast across the country.
The jet, a F-7  BGI, is the final and most advanced variant in China's Chengdu J-7/F-7 aircraft family, according to Jane's Information Group. Bangladesh signed a contract for 16 aircraft in 2011 and deliveries were completed by 2013.
Several hundred pupils demonstrated near the crash site on Tuesday, demanding a thorough investigation and an accurate death count.
The demonstration began as two senior advisers from the interim administration arrived at the scene.
The protesters chanted slogans such as "We want justice" and "Why did our brothers die? We demand answers!" effectively trapping the advisers and several senior officials inside the school building.
In a video message, Bangladesh's interim leader and Nobel laureate Muhammad Yunus promised an investigation into the accident.
"We will definitely investigate this incident, but these innocent children will never come back," he said.
"They are all our children, and they are gone forever. We are ensuring treatment for the injured, and everyone is making every effort for them," he added.
He expressed sympathy for the parents, relatives and friends of the deceased, saying: "To say we are shocked would be an understatement. The scars of this accident have not yet healed."
The crash comes weeks after an Air India plane crashed into a medical college hostel in Ahmedabad in neighbouring India, killing 241 of the 242 people on board and 19 on the ground in the world's worst aviation disaster in a decade.
with DPA and AP
