ALLAHABAD, India — The pilgrims came, millions upon millions of them, in the greatest tide of humanity ever seen. Again and again, the vast crowds threatened to press too close, to trample the smallest. Then it happened.

As many as 30 people were killed Sunday in a stampede at the train station here as they rushed up steps leading to one of the platforms, the police said. The stampede came at the height of the Kumbh Mela, a Hindu religious festival that occurs once every 12 years by the banks of the Ganges and Yamuna Rivers.

“I can’t believe God punished us this way,” said Santos Singh, one of the pilgrims at the station. “My 15-year-old son got injured. I wish police were more responsive.”

About 30 bodies covered in white sheets were visible on the train platform on Sunday evening. Several appeared to be children.