The infants are suffering from "birth asphyxia" or respiratory distress.
"All the four infants in the NCIU who needed both ventilator and incubator support are progressing and responding to treatment," Dean of the Hospital Dr Narayana Babu told PTI.
He also expressed hope that these infants will be taken "off the ventilator in another 24-32 hours positively. Top specialists are attending to the children and they are progressing."
State Health and Higher Education Ministers, Vijayabaskar and Palaniappan respectively, Director of Medical Education, Dr Geetha Lakshmi, specialist in neonatal care, Dr S Srinivasan were among those who have led inspections.
Chief Minister O Panneerselvam said the deaths were due to natural causes. The government took quick steps to handle the situation and have also put in place measures as part of follow-up action, he had said yesterday.