The two men, Abu Bakker Qassim and A'Del Abdu al-Hakim, were cleared last year of being "enemy combatants" and a US federal judge had earlier declared their detention in Cuba unlawful.

Lawyers for the two ethnic Uighurs said they should be released and took the unusual step of appealing directly to the Supreme Court.

It would have taken a rare intervention by the Supreme Court to deal with the case now, but justices refused to hear the case.

The case is problematic for the US authorities as they will only release the men if they can go to a country other than the United States.

No return

They cannot return to China as it is likely they will be tortured or killed.

Uighurs are Turkic-speaking Muslims from the west of China with a language and culture distinct from the rest of the country.

Many Uighurs have been waging a low-level militant campaign for greater autonomy for the region.

As a result Beijing has waged a relentless campaign against what it calls the violent separatist activities of the Uighurs.

Qassim and al-Hakim were captured as they fled a Taliban military training camp where they had been learning techniques they planned to use against the Chinese government.

It had earlier been claimed they were economic migrants heading to Turkey.

Mass appeal

A newspaper report over the weekend said that Germany was being pressed to take the two men.

A Supreme Court lawyer for the Bush administration, Paul Clement, told justices that there were "substantial ongoing diplomatic efforts to transfer them to an appropriate country".

About 500 foreigners are being held at Guantanamo Bay.

Lawyers for more than 300 of the men filed a brief in Monday's case, saying that Qassim and al-Hakim "are far from the only innocent non-combatants languishing at Guantanamo".