A pre-dawn stampede at the world's largest religious gathering killed at least 30 people in India on Wednesday, with many more injured after a surging crowd spilled out of a police cordon and trampled bystanders.

Deadly crowd incidents are a frequent occurrence at Indian religious festivals, including the Kumbh Mela, which attracts tens of millions of devotees every 12 years to the northern city of Prayagraj.

As pilgrims rushed to participate in a sacred day of ritual bathing, people sleeping and sitting on the ground near the rivers said they were trampled by huge swells of devotees coming towards them in the darkness.

"The entire crowd fell on top of me, trampling me as it moved forward," pilgrim Renu Devi, 48, said.

"When the crowd surged, elderly people and women were crushed, and no one came forward to help."

Rescue teams carrying victims from the accident site weaved through piles of clothes, shoes and other discarded belongings.

Police were seen carrying stretchers bearing the bodies of victims draped with thick blankets.

"Thirty devotees have unfortunately died," senior police officer Vaibhav Krishna told reporters during an evening news conference at the festival. "Ninety injured were taken to the hospital."

Krishna's briefing came nearly 18 hours after the stampede and was the first official death toll given by authorities.

Festivities had otherwise been allowed to continue almost as normal during the day, with millions still trekking to the riverbanks to immerse themselves in the water.

Prime Minister Narendra Modi called the stampede "extremely sad" and offered his "deepest condolences" to relatives of those killed. (AFP)