"I think it bears emphasis that the court's decision does not concern military commission trials, which will continue to proceed," he said.
"Instead it addresses the procedures that the Congress and the president [George Bush] put in place to permit enemy combatants to challenge their detention."
The supreme court on Thursday ruled, by a vote of five to four, that detainees in the US jail in southern Cuba "have the constitutional privilege of habeas corpus".
"We'll abide by the court's decision. That doesn't mean I have to agree with it"
"The laws and constitution are designed to survive, and remain in force, in extraordinary times," said Justice Anthony Kennedy, writing for the court.
Mukasey said that he had not yet studied the supreme court ruling and that the government's next move had not been decided.
However he did say that it would comply with the decision.
"We are going to study both the decision itself, and whether any legislation or any other action may be appropriate."
George Bush, the US president, also said that he disagreed with the ruling but would abide by it.
"It's a deeply divided court and I strongly agree with those who dissented ... and their dissent was based on serious concerns about US national security," he said during a visit to Italy on Thursday.
Rob Reynolds, Al Jazeera's senior Washington correspondent, said the ruling was a very significant milestone in this long-running battle.
Explaining that Guantanamo was chosen because it was not on American soil and therefore would be beyond the reach of the American justice system, he said the decision was a victory for the proper system of justice.
The court ruled that even if the base was on Cuban territory, it was in fact operating as if it were on American soil and therefore detainees had the same constitutional rights as all Americans.
The ruling is the third on Guantanamo that has gone against the Bush administration.
Detainees and their legal teams could now demand that the government reveal the evidence against them to justify their continued detention.
The government has refused to do this arguing it would be against the interests of national security.
Detainees have long protested that they had been mistreated, and rights groups have questioned the legality of the Guantanamo Bay military tribunals.
About 270 so-called enemy combatants remain at the prison facility, some who have been held for more than six years.