The newborns — between one and seven days old — had been in the neonatal intensive care unit since Friday.
"We have sent a team to Burla for inquiry. Action will be taken after they submit their report," state health secretary PK Mohapatra said.
Authorities at the hospital, considered to be among the top healthcare facilities in the state, termed the deaths a coincidence.
Hospital superintendent Dr Laxmikanta Das said, "All the babies were critically ill. One of them had brain haemorrhage, another was severely anaemic and the others were underweight." He said one of the babies was referred to the hospital by a private healthcare facility.
Locals, however, alleged the newborns died due to malfunctioning of the incubator in the unit. Thousands of locals assembled on the hospital premises demanding strong action against the hospital staff.