These flights will be operated by Air India and a few private airlines.
Rajali is located around 60 kilometres away from Chennai.
As many as 100 people are still stranded at Chennai airport, which has been shut till December 6, and their evacuation is expected to be completed tonight or tomorrow morning, according to the Ministry.
Briefing reporters about plans to restore flight connectivity from Chennai, Civil Aviation Secretary R N Choubey said a plan is being made to operate at least six flights tomorrow and the day after.
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The proposal is for limited commercial flight operations and not for evacuation of people by operating six flights each over the next two days, Choubey said.
Minister of State for Civil Aviation Mahesh Sharma said the proposed flights from the Rajali naval base would offer tickets at low prices.
"(For these flights) the airlines will charge Rs 1,000 for destinations in the South and Rs 2,000 for destinations in the North," Sharma said.
He, however, said that cusomers booking tickets for these flights would be allowed to carry only handbaggage and not check-in baggage.
Choubey said Chennai airport is safe and so far there has been no report of any damage to aircraft grounded there.
On Wednesday, the Airports Authority of India (AAI) had said 34 aircraft of various airlines were grounded at Chennai airport.
With Chennai airport inundated following heavy rains, Navy's base at Arakkonam is serving as the makeshift airport for supplying relief material as well as for bringing in National Disaster Response Force teams.
Meanwhile the special passenger flight operated today by the national carrier from Hyderabad to Rajali to bring back its 120 starnded passengers is expected to take off from the naval air station at around 2200 hours, an Air India spokeperson said.