Kerala Chief Minister Oommen Chandy said the nurses were on the move in three buses to an unknown destination, believed to be Mosul, a stronghold of the insurgents who have captured large parts of Iraq.
The external affairs ministry said separately that some nurses -- all of them from Kerala -- suffered "minor injuries" during the shifting but that all of them were safe.
Ministry spokesman Syed Akbaruddin said the nurses were "on the road" but there was no information where they were headed to.
He made it clear that they were not being moved on "their free will".
Asked if the insurgents had shifted them forcibly, Akbaruddin said: "In zones of conflict there is no free will. There are no expressions of free will."
Pressed to reveal who had taken them, the spokesman said: "Everything need not be said."
But one of the nurses in Iraq earlier told an Indian television channel that they were being moved by the insurgents to Mosul.
The insurgents had been reportedly telling the nurses over the past three days to leave the Tikrit hospital but the nurses, who were in touch with the Indian mission in Baghdad, had resisted.
On Thursday, however, the insurgents bombed the Tikrit hospital premises, injuring some nurses, in a bid to force them to leave, reports reaching the Kerala capital said.
Some of the family members of the captive nurses told journalists in Kerala that they regretted the lack of adequate action by the Indian government to rescue the nurses.
"We have been told that yesterday (Wednesday) the Bangladeshi embassy officials in Iraq took their nationals in Tikrit to safety," one family member said in Thiruvananthapuram. "Why can't the Indian embassy do what the Bangladesh officials did?"
Spokesman Akbaruddin said the external affairs ministry was in regular touch with the Indian mission in Baghdad and a variety of interlocutors on the ground, both in Iraq and outside.
"They (nurses) agreed to move out... All are safe and unharmed."
The government admitted that it was "a difficult time" for both the Indians stranded in the conflict and non-conflict zones in Iraq. A total of 25 Indian officials were deployed in four Iraqi cities.
So far about 900 Indians had been provided air ticket to leave Iraq, he said. A total of 1,500 Indians were registered with Indian authorities to leave Iraq.
Some Indians working in Iraq had not decided whether they wanted to leave or not. "We are committed to helping every Indian national," the spokesman said.