Sushma Swaraj asserted that it was the government's duty to keep looking for the Indians, given that so far, "there are no bodies, no bloodstains, no list, no ISIS videos."
The group of Indian labourers, mostly from Punjab, was taken hostage by ISIS when it overran Iraq's second largest city Mosul in 2014. The workers were trying to leave Mosul when they were intercepted.
"We can't even take them from the category of 'missing' to 'believed to be dead'. I will not take this crime on my head," Sushma Swaraj said.
"People who are convinced that they are dead and I am lying, they are free to tell their families that they are dead. But if anyone turns up alive, then it is their responsibility," she added.
On Monday, Iraq said it was "not 100 per cent sure" whether the Indians, who were kidnapped by ISIS in Mosul three years ago, are alive or dead.
The government has repeatedly said all efforts are on to find the Indians and without information otherwise, the workers are still considered alive.
One of the captured Indians, Harjit Masih from Gurdaspur, had managed to escape and had claimed to have witnessed the massacre of the others. But the government has rejected it.
"Why should I believe Harjit Masih's claims that the 39 Indians are dead? It is a crime to do this without proper proof," Ms Swaraj said today.