The new administration’s position had been the subject of wide speculation before a court deadline Friday for the administration to tell federal judges what definition it believes the courts should use in the habeas corpus cases reviewing detainees’ cases. Some detainees’ lawyers had hoped for a much narrower definition, perhaps one that would have eliminated simply “supporting” the Taliban or Al Qaeda as a ground for detention.

Such a change, some of the detainees’ lawyers had predicted, could have undercut the government’s justification for holding as many as half of the remaining prisoners, including jihadists captured in Afghanistan who never fought the United States and others who the government has indicated may have had only tangential ties to Al Qaeda or the Taliban.

The new definition did add a requirement that to justify detention a detainee would have to have “substantially supported” Al Qaeda, the Taliban or forces associated with them. But the administration did not define “substantial,” and the detainees’ lawyers said they doubted that the change would help many of their clients.

The filing, which was made in some 40 habeas corpus cases of detainees’ challenging their imprisonment, is expected to be the government’s position in more than 200 such cases and to govern a separate review of all cases outside of court that has been ordered by President Obama.

Some critics of Guantánamo said that Friday’s filing fitted a pattern of recent moves by the administration that seemed intended to undercut continued criticism of Guantánamo but did not make significant changes in detention policy.

They noted that after Attorney General Eric H. Holder Jr. visited the detention camp last month, he proclaimed it “well run.” They said they had been stung as well by a Pentagon report commissioned by the new administration that said last month that the detention camp on the naval base at Guantánamo Bay meets the humane-treatment requirements of the Geneva conventions.

Ramzi Kassem, a detainees’ lawyer who teaches at Yale Law School, said Friday that the new administration had yet to deal effectively either with efforts to release many of the detainees or to improve the conditions at the camp.