Solar Impulse 2 had travelled 26 percent of the way to the tropical US state by 5am GMT, having flown 2,204 kilometres with 6,136 kilometres more to go, according to the project.
That put the plane and its veteran pilot more than 36 hours into the toughest leg of the bid to circumnavigate the planet using only the power of the sun.
"Enjoying every moment of this flight," veteran Swiss pilot André Borschberg tweeted.
"Getting to this point has been challenging," he said.
"This flight will only be a success if we really partner, the airplane and myself."
The experimental solar-powered aircraft left Japan at around 6pm GMT on Sunday — the small hours of Monday local time —after spending a month in the central city of Nagoya.
The propeller-driven plane was originally scheduled to fly directly from Nanjing in China to Hawaii.
But bad weather along the way forced a diversion to Japan that extended for almost the whole of June as forecasters waited for
A live video feed showed the pilot wearing a thick flight jacket and breathing apparatus.
The temperature in the unpressurised cockpit at one point fell to minus 6C as Borschberg ascended to 8,500 metres above the water.
The journey to Hawaii was expected to take at least five days.
Solar Impulse 2 set off from Abu Dhabi earlier this year in a multi-leg attempt to fly around the world without a single drop of fuel.
The aircraft has 17,000 solar cells and on-board rechargeable batteries with a top speed of 140 kilometres an hour.
Its wingspan is longer than that of a jumbo jet but it weighs only 2.3 tonnes — about the same as a car.
The plane is the successor to Solar Impulse, which managed a 26-hour flight in 2010, proving its ability to store enough power in lithium batteries during the day to keep flying at night.