Four deaths were reported from Ganjam district, Odisha's coronavirus hotspot, while Khurda and Cuttack accounted for the remaining fatalities, he said.
"Regret to inform the demise of six COVID positive patients while under treatment," the department said in a statement.
Many of the deceased were suffering from diabetes, hypertension and other ailments, the official said.
Of the 616 fresh cases, 415 were detected among those in quarantine, while 201 are local-contact infections, he said.
Ganjam, Chief Minister Naveen Patnaik's home district, reported 283 of the fresh cases, followed by Koraput (50) and Nabarangpur (40).
Odisha now has 4,896 active cases, while 8,750 people have recovered from the disease so far.
The Health department has tested a total of 3,41,537 samples thus far, the official added. AAM RBT IJT