Fossett was in the 10th day of his attempt to be the first to fly around the world non-stop in a balloon. His last reported position was 500 miles north-west of New Caledonia and about the same distance from the Australian coast.
At the weekend, the Chicago financier broke his own earlier record for distance travelled in a balloon when he reached the halfway point in his circumnavigation attempt.
As the 54-year-old millionaire flew over the small beach town of Geraldton, Australia, he was seen poking his head over the gondola to view the last continent he will cross before heading across the Pacific Ocean towards South America.
Fossett then told mission control in St Louis it was going well. "I was very worried over the Indian Ocean, that I would be caught and captured by the high-pressure area and never be able to get out of it," he said.
His ground crew burst into applause on learning he had travelled 10,480 linear miles, breaking his own record of 10,360 miles set in January 1997. This is his fourth attempt to circumnavigate the word.
A balloon has no way to propel itself or steer, and moves by climbing or descending into winds going in the desired direction. That makes the meteorologists on the crew vital to the flight's success.
Fossett has communicated with his crew by e-mail, using a computer that transmits to a satellite, getting immediate reports on how to avoid winds that could blow him off course.
Earlier, Alan Blount, director of mission control at Washington University in St Louis, said although the trip was going well there was concern Fossett might run out of oxygen before making it to South America, from where he took off eight days ago. However, it was thought the balloonist would have enough to finish the quest, which was expected to take at least six more days.
To circle the globe officially, Fossett must land anywhere east of Mendoza, Argentina, from where he lifted off on 7 August. He has some way to go before he breaks the record for the longest-lasting balloon flight. That record, of nine days, 17 hours and 55 minutes, was set in January by a Swiss pilot, Bertrand Piccard. He was forced to abandon his round- the-world attempt when China refused to let him cross its airspace.
Fossett had said that if he was successful, he would donate half his $1m prize to Washington University.