He said authorities believe the bodies belong to two IOC employees who have been missing since the inferno began.
"We don't expect any more bodies to be recovered," Soni said.
Eight other people died in the blaze, including three more employees, and their bodies had been recovered from the scene, officials said.
Between 1,000 and 1,500 people remain evacuated from the area, but other residents living close by have started to return home, Soni said.
Flames to die out
Firefighters abandoned earlier attempts to extinguish the blaze and expect the flames to die out in the coming days.
Local residents reported hearing a large explosion when the blaze began, engulfing about 50,000 kilolitres of fuel stored in tanks and pouring thick black plumes of smoke into the sky.
IOC officials estimated the cost of the fire at up to 1.5bn Indian rupees ($30 million).
It caused damage to at least 200 small and large industries nearby, the Press Trust of India reported.
The depot, located a short distance south of Jaipur, provides storage for petrol, kerosene, and diesel fuel for several state-owned oil companies.