Thus a new trial would not violate Mr. Burdine's constitutional rights, according to the order.
The opponents argue that trials of this sort violate the time-honored legal principle that there is no punishment without a law.
The trials violate provisions of Geneva Conventions that apply during war and occupation.
In March 1963, the Supreme Court overturned his conviction, holding that his trial violated the 6th and 14th Amendments.
Amnesty International said the trial had "clearly violated international standards for fair trial".
He argued that the second trial would violate his constitutional right against double jeopardy.
But the court did not reject outright Mr. Beckwith's claims that a third trial would violate his constitutional right to a fair and speedy trial.
A presidential statement said that keeping Afghan citizens imprisoned without trial violates the country's constitution, as well as international human rights conventions.
The defendants had said a new trial would violate their Fifth Amendment rights against being tried twice on the same charges.
In the 1960's and 1970's, federal courts asserted a broad power to hear claims by state prisoners that their trials had violated the Constitution.