Washington (CNN) -- The Supreme Court has again refused to review the limits of liability involving the secret detention of a suspected terrorist under the government's post-9/11 "extraordinary rendition" program.

In a separate case, the court turned aside a challenge to the use of the phrase "so help me God" as an informal part of the presidential oath of office.

In the "extraordinary rendition" case, the justices without comment on Monday rejected the petition of Binyam Mohamed and four other men, each of whom claims he was "forcibly disappeared and transported to arbitrary detention and torture on flights" arranged by a private government contractor at the behest of the Central Intelligence Agency. The high court's order stops a pending lawsuit.

At issue is when federal courts can intervene when the White House invokes the "state secrets privilege," preventing disclosure of sensitive or national security information. The high court has not fully examined the state-secrets privilege since 1953, when it affirmed the government's ability to limit public release of certain types of evidence.

The justices have in recent years turned aside numerous challenges to the doctrine when it involves executive branch actions in the war on terror.

The Bush administration initially intervened in the case on behalf of itself and a Boeing aircraft subsidiary, seeking dismissal of the lawsuit on the basis of the state secrets privilege. The Obama administration has continued the government's effort to dismiss the entire lawsuit, claiming the very subject matter is a state secret.

The current lawsuit was brought by the American Civil Liberties Union on behalf of the five former detainees. The lead plaintiff, Mohammed, is an Ethiopian native arrested in Pakistan in 2002. Court records show that after three months in prison, he was secretly transported by a private U.S. chartered jet to Morocco.

Security agents of that country allegedly tortured Mohamed for the next 18 months to gain information about terror activities. He says he was routinely beaten to the point of unconsciousness, was cut with a scalpel all over his body, and had hot liquid poured on him.

ACLU lawyers say other terror suspects were routinely sent to other nations for secret detention and questioning as a way to prevent direct U.S. involvement in what the human rights group calls torture of enemy combatants, which is banned under federal and international law.

CIA officials later acknowledged the rendition program, but refused to discuss details and denied violating any laws.

Mohamed was later turned over to U.S. authorities and eventually wound up at the military prison at Guantanamo Bay, Cuba. A Pentagon report said he admitted training at Al Farouq terrorist camp in Afghanistan, but later recanted, claiming the evidence against him was obtained from torture during the "extraordinary rendition."

He was freed in 2009 and now lives in the United Kingdom, where he is a legal resident. He and fellow onetime prisoners then sued the British and American governments, as well as Jeppesen Dataplan, the Boeing aircraft subsidiary accused of arranging the overseas flights for the CIA.

"I have been through an experience that I never thought to encounter in my darkest nightmares," Mohamed said in 2009, when the lawsuits were filed. "It is still difficult for me to believe that I was abducted, hauled from one country to the next, and tortured in medieval ways -- all orchestrated by the United States government."

There was no immediate reaction from the ACLU over the end of the lawsuit.

The Supreme Court is currently considering an unrelated case dealing with the limited application of the state secrets privilege, over the right of private military contractors to access government information. The Obama administration in that dispute is suing Boeing to recoup millions of dollars from a Navy aircraft that was canceled before ever being built.

The government had argued the sensitive technology on the aircraft allowed it to invoke the state secrets privilege, which has kept the case from going to trial. The contractors countered that has prevented them from fully arguing their claim that they should not have to repay the government for the failed A-12 Avenger. A ruling is expected in that case in a few weeks.

The terrorism case rejected Monday is Binyam Mohamed v. Jeppesen Dataplan, Inc. (10-778).

In the presidential oath of office case, the justices turned aside a legal challenge indirectly involving one of their own. The high court blocked an ongoing legal dispute over the use of religious references during the presidential inauguration ceremony.

Michael Newdow, a California atheist and lawyer, had sued participants in President Obama's 2009 swear-in, including the man who administered the official oath of office, Chief Justice John Roberts. Roberts has pulled out of considering Newdow's lawsuit.

Every oath since 1932 has ended with the phrase "so help me God," repeated by the president. Article II, Section I of the Constitution's original wording of the oath does not include that phrase: "I do solemnly swear (or affirm) that I will faithfully execute the office of President of the United States, and will to the best of my ability, preserve, protect and defend the Constitution of the United States."

Newdow's lawsuit was supported by about 250 individuals and groups who said any mention of God or religion in such events violates the constitutional principle of separation of church and state.

At issue was whether, as a private citizen, the California resident had "standing," or authority, to challenge the ceremony over any personal harm he may have suffered from the inauguration.

A federal appeals court had rejected his earlier arguments. The 2009 ceremony at the U.S. Capitol also included speeches by two clergymen, the Rev. Joseph Lowery and Pastor Rick Warren. Seven of the nine current justices, including Roberts, attended the January outdoor inauguration for the nation's first African-American president.

The high court in March rejected Newdow's separate lawsuit attempting to remove the phrase "In God We Trust" from U.S. currency. The justices in 2004 also ruled against Newdow's effort to block his school-age daughter from reciting the Pledge of Allegiance in class over his objection to the phrase "under God."

The case rejected Monday is Newdow v. Roberts (10-757).