Of these, the Punjab government has submitted a list of 514 people from the state who are stuck in Iraq while Haryana officials said families of 147 people have provided details of their near and dear ones stranded there.
Six youths from Punjab's Gurdaspur district returned to their homes Saturday from Iraq.
Official sources said many more people from both states could be stuck in Iraq as some families have still not contacted the two state governments.
Punjab's NRI Affairs Minister Tota Singh said Punjabis in Iraq were safe. However, he said the central government should arrange their safe exit as soon as possible as conditions in Iraq were worsening every day.
External Affairs Minister Sushma Swaraj Saturday called up Punjab Chief Minister Parkash Singh Badal and assured him that all Punjabis in Iraq were safe.
Of those from Punjab stuck in Iraq, the highest number of 224 was from Hoshiarpur district followed by Jalandhar (40), Ropar (37), Gurdaspur (36) and Patiala and Kapurthala (35 each). The rest are from other districts in Punjab.
Over 40 Indians, mostly from Punjab, were kidnapped by insurgents June 11 in northern Iraq's Mosul town.
Most Indian workers in Iraq are construction or skilled workers.
In Haryana, of the 147 people stuck in Iraq, the highest numbers were from Yamunanagar, Kurukshetra, Ambala and Karnal districts.
The North American Punjabi Association (NAPA) Sunday demanded that the Punjab and central governments should announce a grant of Rs.10 lakh to each worker returning from Iraq to rehabilitate them and start a new life in Punjab.
NAPA executive director Satnam Singh Chahal said the people returning from Iraq needed help for rehabilitation.