In a forceful statement in the Lok Sabha, Swaraj rejected allegations that she misled the country on the issue and said the government will continue its efforts to trace them until getting evidence of their death.
"We will continue our efforts to trace them till the time we get evidence that they are dead, as declaring dead them without proof will be a sin and I will not commit that sin," Swaraj said.
Her strong assertion on the issue came two days after Iraqi Foreign Minister Ibrahim al-Jaafari said here that there is no "substantial evidence" on whether the Indians are alive or dead and confirmed that the prison at Badush, their last known location, has been demolished by terror group ISIS.
However, the Congress appeared to be not satisfied with her statement as its leader Mallikarjun Kharge said, "we will give a notice to discuss foreign affairs and then we will see what you (Swaraj) had said in 2014."
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Earlier, the external affairs minister, referring to a statement she made in Lok Sabha in November 2014, said whatever she did in the case was with consent of the House.
Swaraj on July 16, based on information gathered by her junior minister VK Singh during his recent visit to Iraq, had stated that Badush jail in northwest Mosul was the last known location of the Indians.
In her statement today, she said she never said that the Indians were in the jail and that as per information, they were taken to Badush in early 2016.
The Iraqi foreign minister also had said that ISIS had seized control of Badush jail and it was demolished.
Swaraj said she told her Iraqi counterpart that she will not accept anything on the issue without "proof" and requested him to continue search for them.
The external affairs minister cited an example of the Congress government declaring a soldier martyr in 1971 war and after 45 years, it was found that he was in a jail in Pakistan.
Referring to demolition of the Badush jail, she said she had suggested to the Iraqi foreign minister to look for the jail warden and find out from him details about the Indians. She said even list of prisoners will help.
"Our questions are like if the jail was demolished, then were the Indians there and whether the inmates were killed. If they were killed, where are the bodies...Is there any blood trail," she said.
The external affairs minister said she had never misled Parliament or the families of the abducted Indians.
"I have never misled. I want to ask the opposition what benefit will I get by misleading. What benefit my government get by misleading the people on the issue," she asked.
Swaraj said one person Harjit Masih, who was also abducted along with the 39 Indians but had managed to flee from captivity, had said the Indians were killed but six sources had told the government that they are alive.
Mentioning about her earlier statement, Swaraj said, "I had said that one person said the 39 Indians were killed while six sources said otherwise. I had asked should I go ahead believing the six sources. I had said then that I do not have proof of their being alive," she said.
The government, Swaraj said, has been in touch with countries of the region including Turkey which can help India in the case.
India had requested Iraq to locate the 39 missing Indians, mostly from Punjab, after Iraqi forces recaptured Mosul from ISIS.