Prime Minister Narendra Modi offered his condolences on Twitter. “Distressed by the train accident in Odisha,” he wrote. “In this hour of grief, my thoughts are with the bereaved families. May the injured recover soon.”

Mr. Vaishnaw told the Indian news agency ANI that he had ordered an investigation to determine the cause of the crash.

Indian news reports said that as news of the crash spread, along with reports of mounting casualties, desperate relatives went to Howrah Station in West Bengal, where one of the trains had been heading, eager to determine the status of their loved ones.

At Howrah, one man, Sapan Chowdhury, told The Indian Express he was relieved to learn that his 23-year-old daughter was alive, though she had been injured by glass shards.

India’s trains transport more than 13 million people a day, according to Indian Railways, but the system has been buffeted by years of neglect. In 2014, there were more than 27,000 train-related deaths, according to the country’s National Crime Records Bureau. In 2012, a committee appointed to review the safety of the rail network cited “a grim picture of inadequate performance largely due to poor infrastructure and resources.”