WASHINGTON (CNN) -- Appeals from seven detainees at the Guantanamo Bay military prison in Cuba, contesting their open-ended custody, were turned aside by the Supreme Court on Monday.

Without comment, the justices refused to take a fresh look at the "habeas" petitions by the suspected foreign enemy fighters and what rights they have to make their claims in federal court.

In the so-called Boumediene ruling in 2008, the high court said "enemy combatants" held overseas in U.S. military custody have a right to a "meaningful review" of their detention in the civilian legal justice system. It would force the government to present evidence and justify keeping the prisoners indefinitely, without charges.

But a federal appeals court in Washington has since refused to order the release of any detainee filing a habeas corpus writ, in some cases rejecting such orders from lower-court judges.

According to Pentagon figures, 169 foreign men are still at the Guantanamo facility, including five "high-value" suspected terrorists from the 9/11 attacks set to go on military trial.

"By refusing to hear these cases, and any Guantanamo cases since its 2008 Boumediene decision, the Court abandons the promise of its own ruling guaranteeing detainees a constitutional right to meaningful review of the legality of their detention," said Vincent Warren, executive director of the Center for Constitutional Rights, or CCR, which filed the appeals on behalf of the seven prisoners.

"For nearly 10 years, the Supreme Court's involvement has been essential in checking the excesses of Executive-Branch detainee policy and in clearing a path in the lower courts for justice for the detainees. The [Supreme] Court's refusal to get involved at this critical juncture permits the Court of Appeals to continue to rubber stamp the military's decision-making, undermining our constitutional system of separation of powers."

Among the detainees is Adnan Farhan Abdul Latif, a Yemeni national who has been at Guantanamo for a decade. A federal judge had ordered his release, but the appeals court subsequently concluded that he was "part of" the al Qaeda terror group and that the government could detain him indefinitely.

His lawyers say he went to Afghanistan and Pakistan for medical treatment for a head injury, but the U.S. military-- without revealing too many specifics publicly-- said he was there to train as a terrorist in a remote al Qaeda camp.

At issue were how federal courts should discern the reliability of intelligence reports gathered against individual prisoners, and how far those courts could second-guess the "presumption of regularity" by military interrogations used to gather the information. CCR and other human rights groups have complained the military's interrogation techniques have been too physically and mentally harsh, crossing often into torture, raising questions about the reliability and legitimacy of evidence later used to justify continued detention.

The Obama administration, like the Bush White House before, has repeatedly urged the high court to stay out of detainee issue, since the 2008 ruling.

The appellate court also overturned a previous order to release Hussain Almerfedi, saying even circumstantial evidence that he was a terrorist was enough to confine him.

In the Latif decision last October by the D.C. Circuit of the U.S. Court of Appeals, Judge Janice Rogers Brown, appointed to the court by President George W. Bush, criticized the 2008 Boumediene ruling as based upon "airy suppositions." She suggested the military remained in the best position to decide whether Guantanamo prisoners were being held properly and for how long.

But in dissent, Judge David Tatel, a Clinton appointee, said his colleagues on the D.C. Circuit had "moved the goal posts," calling the "game in the government's favor."

The high court gave no reason why it refused to get involved again in the detainee issue, which the prisoners' advocates said was their best chance to force another constitutional showdown raised by the seven men.

The Center for Constitutional Rights called on President Obama to release 87 Guantanamo detainees the military has determined no longer pose a national security threat to the United States.

The cases are Al-Bihani v. Obama (10-1383); Uthman v. Obama (11-413); Almerfedi v. Obama (11-683); Latif v. Obama (11-1027); Al-Kandari v. U.S. (11-1054); Al-Madhwani v. Obama (11-7020); and Alwi v. Obama (11-7700).

Jose Padilla case

In a separate case, the justices also declined to get involved in the appeal of a convicted terrorist -- an American citizen held for years as an enemy combatant.

Jose Padilla and his mother had sued, seeking to hold accountable former Bush administration officials for his solitary confinement in military custody. Among those accused was onetime Defense Secretary Donald Rumsfeld.

At issue was whether federal officials could be held legally responsible for the "torture" of a citizen on American soil.

Padilla was originally arrested a decade ago, accused of planning to set off radioactive "dirty bombs" in the United States.

The military had held the Chicago native for 3½ years as an enemy combatant, and he hadn't been charged in the alleged plot. That detention prompted Padilla in 2008 to file a lawsuit alleging that the administration's "unlawful" policies violated his constitutional rights as a U.S. citizen. He said he suffered severe physical and mental abuse during his years of isolation in military detention. Similar lawsuits against other officials have been dismissed by lower courts.

The Supreme Court in 2004 had heard Padilla's original appeal over his enemy combatant status, claiming he deserved a chance to contest his military detention on constitutional grounds.

He was arrested in May 2002 at Chicago's O'Hare International Airport as he returned from overseas, where he had been living. He was detained as a material witness in the investigation of the September 11, 2001, terrorist attacks.

President George W. Bush designated him an enemy combatant the following month and turned him over to the military. He was one of the few terrorism suspects designated by the United States as an enemy combatant since 9/11. Padilla was then held in a South Carolina naval brig before the government transferred him to civilian custody and brought criminal charges against him.

The Obama administration has since abandoned using the term "enemy combatant."

The current White House has been criticized for continuing many of the anti-terrorism policies of the Bush administration, including military prosecutions of high-value suspected terrorists held at the U.S. Navy base at Guantanamo Bay.

The case is Lebron v. Rumsfeld (11-1277).