The flight is being operated by Alliance Air, a subsidiary of Air India. The airline has deployed its 42- seater ATR plane on this sector.
He also inaugurated flights on the Kadapa-Hyderabad and the Nanded-Hyderabad sectors through a video conference.
The prime minister also announced that the next flight to take off under the scheme would operate on the Mumbai-Nanded sector.
Later, he laid the foundation of the Hydro Engineering College at Bilaspur online.
Modi said earlier it was believed that air travel was meant only for the "Raja-Maharaja and elite class". Even the mascot of Air India was a maharaja, he said.
The prime minister recalled that he had raised this issue with Rajiv Pratap Rudy, civil aviation minister in the Atal Bihari Vajpayee government, and said cartoonist R K Laxman's Common Man should be the mascot of the airline.
Modi said better connectivity would help the country's youth who, given the opportunity, could change the "fate and picture" of India.
He said in the absence of any aviation policy in the last 70 years, a large number of air-strips constructed during the second world war were lying idle.
These airports would be put to use under a policy formulated by the government and 30 such airports would start commercial operations, Modi said.
He said that the air fare had been capped under the UDAN scheme and would cost less than taxi fare. Travel time would be cut down from hours to minutes, Modi said.
"The Delhi-Shimla flight is cheaper than a taxi ride. A taxi will take at least nine hours and is available for a fare of Rs 10 per km. A flight will now cost you Rs 6-7 per km on the same route and will also save you time," he said.
Advising airlines to start a circular route connecting Nanded Sahib, Amritsar Sahib and Patna Sahib, the prime minister said it would attract Sikhs from all over the world.
Regional connectivity will bring development to tier-2 and tier-3 cities which are becoming "growth engines", said the prime minister.
This will also enhance connectivity to the north-eastern region, he added.
"The scheme will also contribute to national
integration. Different cultures and traditions will be able to intermingle," Modi said, voicing the slogan "Sab ude, sab jude (let everyone fly and unite)."
Jayant Sinha tweeted, "UDAN all set to unify India as its soaring wings of regional air connectivity span across 70 airports."
At the inauguration of the Hydro Engineering College, the prime minister said the institute at Bilaspur would help in providing specially trained manpower for the hydro power sector which has the potential of generating over 1.5 lakh MW of power.
It is a unique fusion of air power and water power on Thursday, he said.
Himachal Pradesh Governor Acharya Devvrat, Chief Minister Virbhadra Singh, Union Health Minister J P Nadda and Leader of the opposition in the HP Assembly P K Dhumal received the prime minister, who was accompanied by Union ministers Ashok Gajapathi Raju and Jayant Sinha at the Jubberhatti airport.
The prime minister arrived here in an IAF chopper from Chandigarh.
Later, he flew to the Annandale helipad by the chopper and drove straight to Shimla's Ridge, the venue of a rally.
With the UDAN scheme, the government aims at connecting 45 unserved and under-served airports and make flying affordable by capping fares at Rs 2500 per seat/hour.
Five airlines were awarded 128 routes under the scheme last month after a bidding process.
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