The government has said it intends to try 60 to 80 of those still in detention under war crimes tribunals.
"We would like to move towards the day when we can eventually close Guantanamo. We do not want to be the world's jailer," said Pentagon spokesman Navy Cmdr. Jeffrey Gordon.
Matthew Waxman, a former senior Defense and State Department official who dealt with detainee policy, has argued strongly for the closure of Guantanamo but he said the Supreme Court's decision could "cut both ways."
If inmates were seen to have the same rights in Guantanamo Bay as on the U.S. mainland, then there could be little strategic reason to move them.
"The major criticism of Guantanamo is that it represents a so-called legal black hole," said Waxman, now a professor at Columbia Law School in New York.
Bush and other senior U.S. officials, including Defense Secretary Robert Gates and Secretary of State Condoleezza Rice, have said they want Guantanamo Bay closed but they point to logistics and other problems.
There is also a drive to announce the closure before Bush leaves office rather than have his successor claim credit.
All of the candidates for November's presidential election - Democratic Sens. Barack Obama and Hillary Clinton and Republican Sen. John McCain - have expressed a wish for Guantanamo to be closed.
While the policy decision for the closure could be taken by this administration, it will be up to them to implement it.
White House, Defense, Justice and State Department lawyers are still arguing the options, including the transfer of detainees to high security military prisons in the United States, moves that will be opposed by local politicians.
The Justice Department is concerned that transferring the detainees to the United States would result in an onslaught of litigation from detainees who would try to use the U.S. justice system to seek their release.
One option is the Disciplinary Barracks at the Fort Leavenworth Army base in Kansas, but the state's senior Republican senator, Sam Brownback, has made clear he will fight that. A naval facility in South Carolina is also being considered.
Senior U.S. officials also hope countries reluctant so far to take home their own detainees will step forward once the U.S. government makes clear its intention to close the prison.
"Our allies talk a lot about concern of Guantanamo Bay but when they are asked to take their foreign nationals back, then they tend to stop talking," said Johndroe.
