Reaching speeds of nearly 400 mph, his experimental single-engine GlobalFlyer took him over Libya, Egypt and the Red Sea on Tuesday before racing into Pakistani air space and continuing east.
By late Tuesday, the aircraft had consumed 25 percent of its 18,000 pounds of fuel, and Fossett had downed at least three diet chocolate milkshakes. The jet took off after sunset Monday from Salina.
Fossett was in "remarkably good spirits for someone who's been awake now for, pretty continuously, over 24 hours," project manager Paul Moore said in an update posted on Fossett's Web site.
Fossett can use autopilot when he needs rest. His mission control in Salina constantly monitors his altitude and course positioning and can call him by phone if something goes wrong.
Fossett estimated he will complete the 23,000-mile journey at midday Thursday.
Fossett, 60, already holds the record for flying solo around the globe in a balloon, as well as dozens of other aviation and sailing records.
Project manager Paul Moore said Fossett reached his cruising altitude of 45,000 feet over the Atlantic instead of over Saudi Arabia, as originally expected, because of better-than-expected performance of the GlobalFlyer.
The project is being financed by Virgin Atlantic founder Sir Richard Branson, a longtime friend and fellow adventurer.
For a while early Tuesday, Fossett was flying blind and in the dark over the U.S.-Canada border after experiencing difficulties with his global positioning system. Moore said Fossett relied on help from mission control to navigate before the problem corrected itself.
"It was a minor scare that could have been a real show-stopper," Moore said.
Fossett is trying to break several aviation records, including the longest flight by a jet. The record is more than 12,000 miles, set by a B-52 bomber in 1962.
Aviation pioneer Wiley Post made the first solo around-the-world trip in 1933, taking more than seven days and stopping numerous times. The first nonstop global flight without refueling was made in 1986 by Jeana Yeager and Dick Rutan, brother of GlobalFlyer designer Burt Rutan.
In 2002, Fossett became the first person to fly a balloon solo around the world.