Kumar said: "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."
He said, the two men, whose identities are not known, boarded the Samjhauta Express when it left New Delhi on Sunday but soon afterwards began arguing with the conductor, saying they were on the wrong train, and were allowed to jump from the train when it slowed down.
Both countries have condemned the attacks.
Khursheed Kasuri, the Pakistan foreign minister, arrived in the Indian capital on Tuesday for long-planned peace talks.
Guarded by dozens of heavily armed soldiers, he visited victims of the train fire at a New Delhi hospital just after his arrival and later said he planned "to carry the peace process forward".
Two bombs, hidden in suitcases, exploded on Monday on board the Samjhauta Express train as it travelled from New Delhi to the northern Pakistani city of Lahore, sparking a 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
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Two other bombs planted on the train failed to explode.
The Samjhauta Express goes from New Delhi to the border town of Atari without stopping, and the fact that the two men were allowed off has raised concerns of lax security measures on the train and at railway stations.
Kumar also said that 13 passengers made it to the Pakistani side of Atari without passports.
"There is no security at all at the station," said a relative of one of the train's passengers.
"There are only a few rude constables and all they're looking for is a few hundred rupees. They don't check anything."
Lack of equipment
Only a few hours after the blast, Lalu Prasad, India's railway minister, had said: "Though there are metal detectors, we don't have the equipment to check what is inside the luggage. We can't deny that."
Kumar said police were also questioning a Pakistani national whose name he gave as Usman Mohammed, who he said claimed to have thrown one of the suitcases off the train.
"The suitcase was thrown on the track," said Kumar. "Usman was there and said he had thrown it. We are verifying it. We are not giving a clean chit [bill]. He was drunk."
As on most Indian trains, the windows of many of the carriages were barred for security reasons and officials said at least one door was fused shut by the heat.
As a result, witnesses said victims remained trapped in the burning carriages for up to 30 minutes.
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.