These companies also buy products from refiners including Reliance Industries, Nayara Energy and Mangalore Refinery and Petrochemicals Ltd to meet local demand.
But declining consumption is forcing state refiners, which together own about 60% of India's 5 million barrel per day (bpd) refining capacity, to reduce the amount of crude they process as storage facilities fill up with unsold products.
Top refiner Indian Oil Corp and its subsidiary Chennai Petroleum has cut refinery runs by an average of 15% to 20%, sources familiar with the matter said.
"About 65% of the crude is used to produce jet fuel, petrol and diesel ...demand for these products is very low," one said.
Another source said: "IOC's has storage capacity but that is used for operational requirement and not for demand management."
The sources asked not to be identified as they were not authorised to speak to media. IOC did not respond to a Reuters email seeking immediate comment.
India's second biggest state-refiner BPCL cut crude processing by "significant" amount next week if consumption continued to fall, BPCL's head of refineries R. Ramachandran told Reuters, adding diesel and petrol consumption tumbled in recent days.
"If the lockdown continues we are staring at double-digit decline in jet fuel, petrol and diesel demand in March, which will necessitate cut in our refinery throughput," he said.
Fuel sales in first two weeks of March fell 10% year on year.
"This is an extraordinary situation it has not been seen earlier," said M.K. Surana, chairman of HPCL, which will cut crude processing by 10% to 20% at its Mumbai refinery as it faces a problem storing bitumen.
Unlike petrol and diesel that can be supplied across the country by pipeline, refiners rely on trucks to transport bitumen, which is used to build road.
Surana said HPCL's Vizag refinery was still running at full capacity but said this was only like to last a few more days.
MRPL, which is based in southern India and sells products to state fuel retailers and usually exports its surplus, said it was dealing with an "unprecedented" fall in demand from state fuel retailers.
"Even the international market is not favourable for export specially jet fuel," said MRPL Managing Director M Venkatesh.
"MRPL will have to take a significant cut in crude processing. Slowdown in refining processing could begin in early April."
(Reporting by Nidhi Verma; Editing by Jason Neely and Edmund Blair) ((firstname.lastname@example.org; +91 11 49548031; Reuters Messaging: email@example.com))