"This is the statement of one of the eyewitnesses... On the basis of the witness we have made portraits of the suspects, of these two people," Kumar said.
On Monday, two bombs in suitcases exploded on the packed Samjhauta Express train connecting New Delhi to the northern Pakistani city of Lahore, sparking the deadly fire.
The suitcases contained bottles of kerosene and petrol, mixed with cloth to prolong the blaze.
"It is a terrorist act, we should condemn this act with unity"
Farzan, Hyderabad, India
Send us your views
Two other bombs were planted on the train but failed to explode.
The attack appeared to be an attempt to undermine a peace process between the two countries.
Kumar said police were also questioning a Pakistani national whose name he gave as Usman Mohammed, who claims to have thrown one of the suitcases off the train.
"The suitcase was thrown on the track," he said. "Usman was there and said he had thrown it. We are verifying it. We are not giving a clean chit [bill]. He was drunk."
Both countries have condemned the attacks. Khursheed Mehmood Kasuri, Pakistan's foreign minister, was due to arrive in India later on Tuesday for scheduled peace talks.
While the attack occurred in India, the majority of the victims on the Samjhauta Express were Pakistanis.
There were 67 bodies at the mortuary in Panipat, many burnt beyond recognition. One other person died in a New Delhi hospital overnight, officials said.
About a dozen people were also injured in the attack.