A mother, centre, cries as she searches for her daughter outside a school in New Delhi on Thursday. (Mustafa Quraishi/Associated Press)

At least five students have died in New Delhi following a stampede at a local school.

Hundreds of students had jammed into a narrow staircase at the state-run school in the Khajuri Khas area in the city's east end Thursday while gathering to write exams, officials said.

"There was a stampede as some of the children on the first floor were asked to come down and others were asked to go up and apparently the staircase was very narrow," Dharmendra Kumar, joint commissioner of the New Delhi police, told the Press Trust of India.

Officials said the two groups of students appear to have collided with one another, sending some youth tumbling to the ground in the tight space.

"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.

The five students who died were girls, officials said.

At least 31 other students were injured, said O.P. Kalra, medical superintendent at the Guru Tegh Bahadur Hospital where the youth were taken. Five of the injured are in critical condition and are on life-support, Kalra said.

"The others are relatively stable and conscious," Kalra said.

Rumour of electrical short circuit

The students killed and wounded in the stampede ranged in age from eight to 16, police said.

About 1,400 students were in the school for the testing at the time of the incident, officials said.

Police said they are still investigating reports from several students that the stampede was triggered when a rumour spread in the crowd that there was an electrical short circuit in the building.

The city was badly waterlogged on Thursday following heavy overnight rains that had caused some flooding.

Parents gathered outside the building following the incident waiting for word on their children. Some of the people gathered threw rocks at the school, a bus and a fire engine, officials said, injuring at least one onlooker.

"We are very sad that five innocent lives have been lost in the accident," Delhi Chief Minister Sheila Dikshit told the Hindustan Times. "Appropriate action will be taken against those found lax in their duty."

An investigation has been ordered into the stampede, said Dikshit, and the families of those who were killed or injured in the incident will be compensated.

With files from The Associated Press