Two Chinese Muslims held by mistake at Guantanamo Bay prison camp learned today that their legal limbo would continue when the US Supreme Court declined to intervene to help them.

Abu Bakker Qassim and A’Del Abdu al-Hakim are Uighurs, Turkic-speaking Muslims who have a language and culture distinct from the rest of China, and who have suffered persecution by the Chinese authorities. They were arrested in Pakistan in 2001 and shipped to the US prison camp along with hundreds of other suspected terrorists.

A year ago, the US military decided that they were not enemy combatants, after hearing that Qassim and al-Hakim were captured as they fled a Taleban military training camp where they were learning techniques they planned to use against the Chinese government.

The men’s plight has posed a dilemma for the courts and an embarrassment for the Bush administration. A federal judge has already ruled that the detention of the two men in Guantanamo Bay was unlawful but that there was nothing federal courts could do.

Lawyers for the two contend they should be released, but the men cannot be returned to China because of the possibility that they will be tortured or killed.

The Bush administration has refused to grant them asylum in the United States, but has been unable to find a country willing to accept the two men, along with other Uighurs. German officials are being pressed to take them, according to a report over the weekend in a newspaper there.

Their plight is unlikely to feature on the agenda when President Bush meets Hu Jintao, the President of China, at the White House on Thursday.

It would have taken an unusual intervention of the Supreme Court to deal with the case now. Lawyers for Qassim and al-Hakim filed a special appeal, asking justices to step in even while the case is pending before an appeals court. Arguments at the US Court of Appeals for the District of Columbia Circuit are next month. The case is Qassim v. Bush, 05-892.

Justices declined, without comment, to hear the case.

Paul Clement, a Bush administration Supreme Court lawyer, told justices that there were "substantial ongoing diplomatic efforts to transfer them to an appropriate country". In the meantime, the men have been given access to television, a stereo system, books and recreational opportunities, including soccer, volleyball and table-tennis, he added.

The detainees’ lawyers painted a different picture, saying that hunger strikes and suicide attempts at Guantanamo Bay are becoming more common and that the men are isolated.

"Guantanamo is at the precipice," Sabin Willett, a Boston lawyer for the two men, wrote in the appeal. "Only prompt intervention by this court to vindicate its own mandate can prevent the rule of law itself from being drowned in this intensifying whirlpool of desperation."

About 500 foreigners are being held at Guantanamo Bay. Lawyers for more than 300 of the men filed a brief in today’s case, saying that Qassim and al-Hakim "are far from the only innocent non-combatants languishing at Guantanamo".

Justices ruled two years ago that the detainees could use American courts to challenge their detentions. And the court this summer will rule on a case testing the goverment’s plans to hold war-crimes trials at Guantanamo Bay.

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