The children, many aged under 12, were about to return home from class on Monday when the Chinese-manufactured F-7 BGI Bangladesh Air Force jet ploughed into their school and burst into flames, trapping pupils in the fire and debris.
The military said it had suffered mechanical failure.
Students from the school and others from nearby colleges protested as two government officials visited the crash site, demanding an accurate death toll and shouting, "Why did our brothers die? We demand answers!".
Elsewhere in the capital, hundreds of protesting students, some of them waving sticks, broke through the main gate of the federal government secretariat, demanding the resignation of the education adviser, according to local TV footage.
Police baton charged them, fired tear gas and used sound grenades to disperse the crowd, leaving dozens injured, witnesses said.
Dhaka Metropolitan Police Deputy Commissioner Talebur Rahman said they had to use tear gas to disperse the protesters.
He said he did not have information on the number of injured.
Rescue workers continued to scour the charred buildings for debris on Tuesday as distressed residents of the area looked on.
Some parents were inconsolable.
Abul Hossain broke down as he spoke about his nine-year-old daughter, Nusrat Jahan Anika, killed in the crash.
"I took her to school yesterday morning like every day. I had no idea it would be the last time I would be seeing her," he said.
She was buried on Monday night.
Rubina Akter said her son Raiyan Toufiq had a miraculous escape after his shirt caught fire when he was on a staircase.
"He sprinted to the ground floor and jumped on the grass to douse it," she said.
"He tore his shirt and vest inside, which saved him from severe burns."
The jet had taken off from a nearby air base on a routine training mission, the military said.
After experiencing mechanical failure the pilot tried to divert the aircraft away from populated areas but it crashed into the campus.
The pilot was among those killed.
On Tuesday, the military said in a statement that 31 people had died and 165 had been admitted to hospitals in the city.
The health ministry said 68 remained in hospital and the condition of 10 of them was critical.
The government announced a day of mourning, with flags at half-mast and special prayers at all places of worship.
Pope Leo said he was deeply saddened to learn of the loss of life in the crash and prayed that families and friends may be consoled in their grief, and for the healing and comfort of the injured, according to a Vatican statement.
The protesting students called for those killed and injured to be named, the decommissioning of what they said were old and risky jets and a change in air force training procedures.
A statement from the press office of Muhammad Yunus, the country's interim administrator, said that the government, the military, school and hospital authorities were working together to publish a list of victims.
It also said the air force will be told not to operate training aircraft in populated areas.
The F-7  BGI is the final and most advanced variant of the Chinese 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.
The Chengdu F-7 is the licence-built version of the Soviet era MiG-21.
