Sushma Swaraj told India's parliament that the construction workers had been executed by the Islamic State group.

Their bodies were found in a mass grave in Badush, northwest of Mosul city, and sent to a local organisation for DNA testing.

"Yesterday they told us that 38 samples had matched. The 39th had a partial match as he didn't have any immediate family," said Swaraj.

The 39 were abducted in June 2014 when IS jihadists overran large swathes of territory in Iraq and captured Mosul.

The victims were mostly from poor families in India's northern Punjab state.

They had been working for a construction company in Mosul when they were rounded up.

The Indian government never received a ransom call or any other direct communication from the kidnappers.

India will send a special plane to bring the bodies back from Iraq, said Swaraj.

"Howsoever painful, the families will get the dead bodies after over three years. This will hopefully bring some closure to the grieving families," she said.