NEW DELHI: Hundreds of students who were jammed into a narrow school staircase panicked and set off a stampede Thursday that left five girls dead and 31 other students injured in India's capital.

Five of the injured were in critical condition, said O.P. Kalra, medical superintendent of the Guru Tegh Bahadur Hospital, where the injured boys and girls were taken.

The stampede occurred early in the day as students arrived for an exam, Kalra told reporters.

Amod Kant, a former police officer and well-known child rights activist, said the students taking the exam were told to move to a higher floor of the school because of heavy rains and flooding on the ground floor. The stampede erupted amid the chaos of moving students up the stairs when others suddenly came rushing down.

"The exams were about to start when suddenly some boys came inside. They pushed us and then we came out. We were coming down the staircase when the stampede took place," student Sanjana Gautam told the Press Trust of India news agency.

The students ranged from 8 to 16 years old, police spokesman Rajan Bhagat said.

By midday, police had sealed off the school to media and parents.

At the hospital, grieving parents were waiting to take home the bodies of their children.

"We rushed to the hospital and we found her dead," said a crying woman who only gave the name of her dead 12-year-old daughter, Aishya Khatun.

Just after the stampede, parents gathered outside the school wailing in anguish. A few threw rocks at the building, news reports said.

Angry residents also hurled stones at a bus and fire engine, injuring one person, before police reinforcements arrived on the scene, witnesses said.

A government investigation was ordered into the stampede, said Sheila Dikshit, New Delhi's top official.