Amid Opposition uproar, she was not able to make the statement in the Lok Sabha.
In order to verify the bodies, DNA samples of relatives were sent to Baghdad, and four state governments - Punjab, Himachal Pradesh, West Bengal and Bihar - were involved in the process.
Ms Swaraj added: "It is unfortunate that the missing persons were not brought back alive, but at least for the relatives and dear ones there is a certain closure of this ordeal that has lasted for nearly three years".
Swaraj earlier said in the Rajya Sabha that their bodies were recovered from Badosh - a village in the northwest of Mosul - and their identities established through DNA testing although it was not immediately known when the Indians were killed.
Forty Indian nationals, who were employed at a construction site in Mosul, were kidnapped by suspected ISIS terrorists in 2014; one of them Harjeet Masih had managed to escape.
"It is my appeal to the Government of India and the Punjab government to provide all possible help and financial aid to families of 39 Indians killed in Iraq", he tweeted. "Masih had escaped along with Bangladeshis with the help of a caterer using a fake name Ali", the minister said.
-Further, he added, that he was shot in his right thigh and fell unconscious covered with the bodies. Everyone around me fell.
"Since the session of the Parliament was on, it was my responsibility to inform the House first", Swaraj said during a press conference.
Manjeet Kaur, wife of Davinder Singh, who is among the dead, told ANI that the government kept telling them all along that he was alive. It was in June 2014 that his family heard his voice for the last time.
Bodies of 39 Indians, who were abducted in 2014, have been identified after DNA matching, India's foreign minister says.
Taking to Twitter, Singh, the minister of state for external affairs said, "We are sorry that we lost them". "We are clueless about what we need to do". We have to talk to the state governments also. She said that they could proceed only after the liberation of Mosul in July 2017. "We gave no false hopes", she said.
In July a year ago, Swaraj had told Parliament that there was no evidence that the missing people had been killed by the Islamic terrorists and that they can't be declared as dead.
PM Modi assured that government tried their best in the search for the missing Indians.
"What Soni had said in Parliament has come true today", he said. He had just a one-and-half-year daughter when he left for Iraq. He had claimed that rest of the 39 abducted Indians had been killed by the ISIS. "The plane carrying the mortal remains will first reach Amritsar, then Patna and then go to Kolkata", Sushma Swaraj said.
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