BEIJING (CNN) -- Three balloonists received good news Tuesday when the Chinese agreed to let their expedition continue flying over China -- provided they leave the country as soon as possible.

Project manager Michael Kendrick announced the development live on CNN even before he had a chance to relay the message to his crew. ( 498 K/30 sec. AIFF or WAV sound)

"We're just so grateful for the Chinese people," Kendrick said from London.

The crew "infringed their airspace and disobeyed their instructions, so they had no choice but to ask us to land," he said. But in respect to the British ambassador, China gave the balloon permission to continue, he later wrote in a statement from the expedition headquarters in London.

The team, composed of British tycoon Richard Branson, U.S. millionaire Steve Fossett and Swedish co-pilot Per Lindstrand, hopes to become the first to fly a balloon nonstop around the world.

As they crossed the Nachma Barwa mountains 40 miles (60 kilometers) into China at about 2000 GMT, the team was plotting the most direct route out of the country, said ICO Global, the mobile telephone company sponsoring the venture.

The balloonists hope to catch a strong wind stream so they can be "somewhere in America" by Christmas Day. But the negotiations with China have cost them precious fuel and time, according to the statement.

Risky Tibetan landing averted

Earlier in the day the Chinese government ordered the aircraft to land, forcing the crew to contemplate a risky night-time landing in remote Tibet. The terrain is "implacably hostile," and landing in its high-altitude, deep freeze would have been a last resort, Kendrick said earlier.

The Chinese Foreign Ministry expressed disapproval that the balloon did not fly through one of two pre-approved, narrow flight corridors at the northern and southern extremes of the mainland.

The balloon has experienced other difficulties since lifting off from Morocco on Friday.

Only intense diplomacy overcame a last-minute decision by Libya to rescind permission to fly over its territory. And the balloon altered its original flight path to avoid thunderstorms over the Mediterranean and British bomb strikes in Iraq.

On Sunday they navigated a narrow corridor that brought them close to three countries that had denied permission to fly over their territories: Iraq, Iran and Russia.

Considerably off course due to the hazards, the crew flew across Turkmenistan, headed into Afghanistan and skirted down along the southern spine of the Himalayas, the highest mountain range in the world, in a fruitless attempt to reach a permissible flight area below the 26th parallel.

China said it was primarily concerned about safety, because of heavy air traffic in central and eastern China, a British official said.

When Chinese authorities contact them, the balloonists will radio Chinese airfields "to ensure the giant drifting balloon poses no danger," according to an ICO Global statement on Tuesday.

In February, China withheld permission for a European balloon team to fly through its airspace, forcing them to land and end their around the world bid.

Former rivals, Branson and Fossett have each made at least four attempts to complete the 24,000-mile (39,000-kilometer) trip, which they estimate could take eight to 20 days.

Another seven crews across the globe are preparing to challenge the team for the record. Four are ready for an attempt this winter.

Reuters contributed to this report.