He said the state government has "committed" land to the Centre for this purpose.
Kumar made the announcement at the golden jubilee celebrations of the Akhil Bharatiye Mithila Sangh at Talkatora Stadium, an event which was also attended by Union Home Minister Rajnath Singh and Lok Sabha Speaker Sumitra Mahajan.
"New airports will be developed in Darbhanga and Purnia. We will make all efforts to develop the Mithila region and promote its language, arts, culture and rich history. The new Patna airport terminal will have Maithili (Madhubani) paintings on its roof," Kumar said.
However, it is not clear whether the Darbhanga and Purnia airports fall under the UDAN scheme.
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The scheme seeks to make flying more affordable for the masses with fares capped at Rs 2,500 per hour of flight.
The first round of bidding for RCS routes took place in March, when five carriers were awarded 128 routes.
Nearly 15 of these routes have commenced operations.
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