Bertrand Piccard, one of two pilots of Solar Impulse 2, said the aircraft's take-off from Ahmedabad city in the western state of Gujarat was delayed by five days because of tedious paperwork.
The plane landed in Ahmedabad last Tuesday from the Omani capital Muscat after completing an initial sea crossing in its epic bid to become the first plane to fly around the world solely powered by the sun.
"The delay is (because of) of administration, papers, stamps," Piccard told reporters before the plane finally took off from Ahmedabad airport on Wednesday morning.
"I'm not here to accuse anybody," a frustrated Piccard said.
"I just say that since the last five days we are trying to get all the stamps and every day (they) say tomorrow," he said.
"Since five days we are desperate to get all the stamps and we still have stamps missing."
The single seater had been due to leave on Sunday for a short flight to the Hindu holy city of Varanasi before heading onto neighbouring Myanmar.
But the plane could only leave on Wednesday following a series of delays, including a last-minute hitch at the time of scheduled take-off that had originally been blamed on poor weather.
Piccard's comments risk embarrassing Modi, who has vowed to cut bureaucratic red tape in promised reforms to revive India's economy after storming to power at general elections last May.
Modi, who was the chief minister of Gujarat before becoming premier, wants to attract more foreign companies who have long complained of encountering bureaucratic nightmares in India.
Modi supporters have often touted Gujarat's business-friendly policies as a model for success which should replicated nationally.
Kiran Mazumadar Shaw, chief of Indian biotechnology company Biocon, on Wednesday took a swipe at Modi's government following the pilot's tirade.
"Hope (the prime minister) heard the solar plane's pilot commenting on bureaucratic delays n cumbersome paperwork...Red tape and petty officialdom are stalling progress," she wrote on Twitter.
The team behind Solar Impulse 2, which has more than 17,000 solar cells built into its wings, hopes to promote green energy with the circumnavigation attempt.
Ridiculed by the aviation industry when it was first unveiled, the venture has since been hailed by UN chief Ban Ki-moon.
Muscat was the first of 12 planned stops on the plane's journey around the world from Abu Dhabi, with a total flight time of around 25 days spread over five months.
The sea legs pose the greatest challenge for the Solar Impulse team as any loss of power over the water would leave the pilot no alternative but to bail out and await rescue by boat.
The longest single leg will see one of them fly solo non-stop for five days and nights across the Pacific from Nanjing, China, to Hawaii — a distance of 8,500 kilometres (5,270 miles).
The plane's maiden leg last Monday took co-pilot André Borschberg 13 hours and two minutes, while Piccard's flight to Ahmedabad of 1,468 kilometres was hailed as the longest point-to-point distance flown by a solar-powered plane.
Borschberg, the CEO and co-founder of Solar Impluse, set the previous record when he flew 1,386 kilometres across the United States.