Indian authorities have ordered a probe into the stampede at the Maha Kumbh Mela Hindu festival that killed dozens of devotees on Wednesday as millions gathered for a "holy dip" in sacred river waters as part of the six-week event, said officials.

Police said 30 people were killed in the crush at the world's biggest gathering of humanity and 90 were injured, but sources told Reuters the death toll was nearly 40.

Some witnesses spoke of a huge push towards the rivers that caused devotees to fall on each other, while others said closure of routes to the water brought the dense crowd to a standstill and caused people to collapse due to suffocation.

"The government has decided that a judicial inquiry of the incident will be done. For this, we have formed a three-member judicial commission," Uttar Pradesh state Chief Minister Yogi Adityanath told reporters late on Wednesday.

"The judicial commission will look into the entire matter and submit its report to the state government within a time limit," he said.

More than 76 million people took a dip at the confluence of three sacred rivers in Prayagraj in the northern state of Uttar Pradesh until 8 p.m. (1430 GMT) on Wednesday alone, officials said.

Nearly 280 million people have attended the festival since it began two weeks ago, including federal ministers, industrialists, and celebrities.

The Hindu festival - held every 12 years - is expected to draw some 400 million devotees in 2025, officials estimate. The Haj pilgrimage in Saudi Arabia, in comparison, drew 1.8 million people last year.

Devout Hindus believe that taking a dip at the confluence of three sacred rivers - the Ganga, Yamuna, and mythical Saraswati - absolves them of sins and brings salvation from the cycle of birth and death.

Opposition leaders have blamed the stampede on mismanagement and urged the government to improve festival arrangements, while local media said on Thursday that better crowd planning was needed to prevent such incidents.

"There is much scope for improving crowd management at the Kumbh," the Hindustan Times newspaper said in an editorial.

"There is no doubt that more personnel have to be deployed, and better planning is needed - using both ground resources and modern technology," it said, adding that a repeat of the tragedy must be prevented at the three 'royal dips' scheduled in coming weeks.

While devotees take 'holy dips' everyday, there are specific dates when the practice is considered particularly sacred and is called a 'royal' dip - Wednesday was one such day and three more are scheduled before the festival ends.