WASHINGTON—The Obama administration on Monday lifted its freeze on new military trials at Guantanamo Bay and for the first time laid out its legal strategy to indefinitely detain prisoners who the government says can't be tried but are too dangerous to be freed.

With the policy shifts, Mr. Obama is acknowledging the difficulty he has faced in trying to close the prison at the Guantanamo Bay Naval Base in Cuba, which he had ordered on his second day in office. He is also responding to a congressional ban of moving detainees...