The Indian embassy in Baghdad has advised the nurses to "try and hold on till Thursday morning".
The nurses had Tuesday refused to board two buses brought by "some English-speaking men" to the hospital compound in Tikrit where they have been stranded for more than two weeks.
But Wednesday, they were being forced to board the buses and were told they would be taken to Mosul, another stronghold of the Islamic State in Iraq and Syria (ISIS).
The nurses were forced to board the buses to go to Mosul
Kerala Chief Minister Chandy, who arrived in New Delhi Wednesday night, said he would be meeting External Affairs Minister Sushma Swaraj over the matter.
Asked about the nurses being told to travel by bus, the chief minister told IANS: "Yes, I am told the people are going by bus."
"I'm contacting the union foreign minister, the Indian embassy in Iraq," he added.
According to a source, the nurses are very worried.
One of the nurses told IANS that they contacted the Indian embassy officials in Baghdad and were "advised to try and hold on till tomorrow morning".
The men who asked them to leave have given the nurses "two hours" to decide and warned that the hospital is going to be bombed, a source told IANS.
The nurses are frightened with the sound of explosions going off around the hospital.
The Iraqi army is locked in a fierce battle with ISIS militants to retake the city.
"Bombs are exploding around the hospital all the time," one of them said.