The US denies it is violating human rights
The challenge, which has been filed by a number of civil rights activists, demands that the US Government brings the suspects before a court and defines the charges against them.
Backed by a former attorney-general, it alleges that the prisoners are being held in violation both of the Geneva Convention and American law.
Stephen Yagman, the civil rights lawyer bringing the action, said the case would force the Bush administration to clarify the men's status.
Alarm
The legal action follows mounting international alarm at the detainees' treatment.
US District Court Judge Howard Matz had scheduled a hearing for 0800 (1600 GMT) on Tuesday on the activists' case.
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He will have to decide whether a US District Court has jurisdiction over prisoners in Cuban territory leased to the US Government, and whether a case brought by LA-based petitioners - a coalition of clergy, professors and civil rights lawyers which includes former US attorney general Ramsey Clark - is valid.
US Defence Secretary Donald Rumsfeld said on Tuesday that the US was treating the foreign prisoners "humanely", and in accordance with international conventions.
"No detainee has been harmed. No detainee has been mistreated in any way," he added.
The leader of the International Red Cross delegation which has been visiting the prisoners, has said he has had good access to them.
Urs Boegli said he had been able to shake their hands and offer them a biscuit and a cigarette.
Mr Boegli declined to comment on the prisoners' condition, but said a team would stay in place to continue monitoring their treatment.
American Taleb
The man people are calling The American Taleb, John Walker Lindh, is due to arrive in the US within the next day or two.
Mr Walker was being held on the US warship Bataan in the Indian Ocean, but he has now been moved to Kandahar in southern Afghanistan.
From there he will be flown to the US to face trial on charges of conspiring to kill US nationals and providing support to the al-Qaeda terrorist network.
EU pressure
America refuses to afford the detainees at Guantanamo Bay the status of prisoners of war, which would grant them rights under the Geneva Convention.
But the European Union has said the US Government must treat the suspected al-Qaeda and Taleban fighters held at its base in Cuba as PoWs.
There was outrage in Europe after the prisoners were photographed wearing orange jump suits, shackled and kneeling, with goggles over their eyes and masks over their mouths and noses as they arrived at the base.
The International Committee of the Red Cross (ICRC) said on Monday that America might have violated the convention by distributing pictures of the prisoners, which were published by media outlets worldwide.
Correspondents say that what worries Washington the most is that if the detainees were classed as PoWs, the Geneva Convention would entitle them to refuse to give their interrogators any information other than their names, ranks and serial numbers.
