More than 200 ambulances were sent to the scene in Balasore district, says Odisha's chief secretary Pradeep Jena.
One passenger train is thought to have derailed before being struck by another on the adjacent track late on Friday.
It is India's worst train crash this century. Officials say the death toll is expected to rise further.
Indian Railways said the two services involved were the Coromandel Express and the Howrah Superfast Express.
Sudhanshu Sarangi, director general of Odisha Fire Services, said that the death toll stood at 288.
Mr Jena said earlier that more than 100 additional doctors had been mobilised.
Indian Prime Minister Narendra Modi said he was distressed by the incident and his thoughts were with the bereaved families.
"Rescue ops are under way at the site of the mishap and all possible assistance is being given to those affected," he tweeted.
Meanwhile, Home Minister Amit Shah labelled the incident "deeply agonising".
One male survivor said that "10 to 15 people fell on me when the accident happened and everything went haywire. I was at the bottom of the pile.
"I got hurt in my hand and also the back of my neck. When I came out of the train bogie, I saw someone had lost their hand, someone had lost their leg, while someone's face was distorted," the survivor told India's ANI news agency.
A day of mourning has been announced in the state.
It is believed that several carriages from the Shalimar-Chennai Coromandel Express derailed at about 19:00 local time (13:30 GMT), with some of them ending up on the opposite track.