The victims were watching a Ravan effigy being burnt at a Dussehra celebration.
The Government Railway Police (GRP) registered an FIR against "unknown persons" and Chief Minister Amarinder Singh announced a magisterial inquiry, which will submit its report within four weeks.
The train that hit the crowds was travelling from Jalandhar to Amritsar. It will take time to identify more bodies as they have been cut into pieces by the metal wheels of the fast-moving train, they said.
One official said the local response was on par with a "war footing" as emergency workers tended to the dead and injured.
It took just about 10-15 seconds for the train to pass - and leave behind a heap of crushed and dismembered bodies.
According to police, a few people angry over the accident attacked their residence, broke window panes and pelted stones on Saturday.
The incident caused an uproar in the state, with attempts by protesters to block the railway route giving rise to clashes with the police.
Women mourn the death of a relative after a commuter train traveling at high speed ran through a crowd of people on the rail tracks, outside a hospital in Amritsar, India, on October 20, 2018. Dussehra celebrations were not held at this spot past year.
Navjot Sidhu said, "This is a very unfortunate accident".
Onlookers rubbished the driver's claims and said the train did not slow down anywhere near the spot. A crisis management group under Punjab health minister Brahm Mohindra has been set up to monitor relief and rehabilitation efforts. He has asked all government and private hospitals to stay open.
Badnore arrived early on Saturday and met the injured at the Guru Nanak Dev government hospital here.
The state chief minister has ordered an inquiry to ascertain whether permission was granted - and by whom.
The minister, who is now in the USA, has cancelled all his engagements there and is immediately returning to India.
He said officials would do "everything possible" to assist the injured. It has been 48 hours since the accident occurred and the police still have no clue about the father and son who remain missing. While some of them were filming the burning of the effigy, others were trying to save themselves. We didn't even get a chance to react.
Former corporator Mandeep Singh Manna, who organised Dussehra celebrations at the same spot in 2015 and 2016, told ThePrint that as the organiser he made sure that he informed the railways about the event.
However, eyewitnesses said the driver despite the presence of the crowd neither sounded a siren nor reduced the speed of the train which was hurtling down at 100 kmph, sources said.
In a tweet, President Kovind said, Indian Railways and local authorities are taking steps to help the affected people.
India's huge railway network is notorious for accidents, including scores who die while crossing the tracks illegally or falling off over-capacity trains.
A large number of people live in the area with homes on both sides of the railway, she said.
There are fears that the death toll is likely to go up further, officials said. The Rapid Action Force is also present in the Joda Patak area.
Nobody should do politics on this issue, he added.
The Punjab Police has deployed its personnel, including commandoes, to manage the crowd.
There was no lighting around the tracks.
Just two minutes before the DMU train crushed the people, leaving 59 dead and almost 60 injured, Howrah Mail had crossed the same spot without a problem with the same number of people standing there.
"People frantically looked for their loved ones".