Johnson Toribiong, reached by phone from the U.S., said Adel Noori left Palau shortly before Toribiong's term ended late last year.
A U.S. official familiar with the situation who asked not to be identified said Toribiong's administration informed the U.S. that Noori, 43, had made arrangements on his own to leave the country.
Noori and the five other men—all of them Uighurs, an ethnic minority that has clashed with China's central government—were released to Palau after spending nearly eight years at Guantanamo Bay. They were captured in Afghanistan and Pakistan in 2001.
The Pentagon determined in 2008 that they were not "enemy combatants" and they were released to Palau on what was billed as a temporary basis the following year.
"I guess the term temporary is a term of ambiguity," said Toribiong.
Uighurs are from Xinjiang, an isolated region of China that borders Afghanistan, Pakistan and six Central Asian nations. They are Turkic-speaking Muslims who say they have long been repressed by the Chinese government.
Noori and his compatriots have said they fear they would be arrested, tortured or executed if sent back to China.
China has said that insurgents are leading an Islamic separatist movement in Xinjiang and wants the men returned.
Ian Moss, a U.S. State Department spokesman, declined to confirm Noori's location.
"We are aware of Mr. Noori's departure from Palau," Moss said. "We are not going to comment on diplomatic discussions with another government or the whereabouts of a private individual."
A local newspaper, Tia Belau, reported earlier this month that Noori had made his way to Turkey to be with his wife and baby. The report also said Noori had transited through Japan, but Foreign Ministry officials in Tokyo said they had no information about that.
Toribiong, who was voted out of office in November, said he feels "a little anxious about the fact that the next president (of Palau) has had to be responsible" for the remaining five Uighurs and their families. There are 14 or 15 of them now living on the island.
"I assumed that I would be able to take care of them and by the end of my term find them a permanent place to go to," he said.
Associated Press writer Kaminsky is based in Olympia, Washington, and has often covered Palau. Follow him at http://www.twitter.com/jekaminsky