It will cross the Arabian Sea to India before heading on to Myanmar, China, Hawaii and New York.
"The adventure has started," Solar Impulse Chairman Bertrand Piccard said emotionally, after pilot Andre Borschberg took off from Abu Dhabi's Al-Bateen airport on the historic circumnavigation aimed at promoting green energy.
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After more than six hours' flying, Borschberg was over the Sea of Oman with nearly 65 per cent of the distance covered.
Meanwhile, the chase plane on which the Solar Impulse team had to travel to Oman to oversee preparations for Borschberg's landing was delayed in Abu Dhabi due to "technical issues," according to their Twitter account.
The take-off by Solar Impulse 2, originally scheduled for Saturday but delayed due to high winds, capped 13 years of research and testing by Swiss pilots Borschberg and Piccard.
Live video streaming on the website monitoring his progress www.solarimpulse.com showed the pilot, wearing an orange jumpsuit, breathing into an oxygen mask.
"From Mission Control Center in #Monaco the engineers are helping me to perform Oxygen Mask tests from #SolarImpulse," he tweeted.
Borschberg had earlier attempted to give media interviews before calling his wife, according to the live feed.
Shortly before take-off, the 63-year-old pilot tweeted that the "challenge to come is real for me & the airplane".
The wingspan of the one-seater plane, known as the Si2, is slightly bigger than that of a jumbo jet, but its weight is around that of a family car.
From Muscat, it will make 12 stops on an epic journey spread over five months, with a total flight time of around 25 days.
Landings are also earmarked for the midwestern United States and either southern Europe or North Africa, depending on weather conditions.
The longest single leg will see a lone pilot fly non-stop for five days and nights across the Pacific Ocean between Nanjing, China and Hawaii, a distance of 8,500 km (5,270 miles).
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