The statement did not identify the two detainees. There are as many as five Algerians at the prison who were recommended for transfer by a task force in early 2010. In all, 86 of the 166 detainees remaining at the prison have been recommended for transfer if security conditions can be met. President Obama has recently sought to revitalize his administration’s effort to close the Guantánamo prison amid a widespread hunger strike.

Mr. Obama had pledged to close Guantánamo within a year of taking office and criticized the prison as overly expensive and a symbol used in terrorists’ propaganda. But his efforts have been strongly opposed in Congress, which in January 2011 imposed requirements that countries be capable of taking steps to control any former detainees and prevent them from terrorist activities.

Republicans have sought to portray Mr. Obama’s efforts to wind down operations at the detention center as soft on terrorism, and on Friday, Senator Saxby Chambliss of Georgia, the ranking Republican on the Senate Intelligence Committee, accused Mr. Obama of taking the risk of releasing detainees who might engage in terrorism, as some released detainees have done, “just to satisfy a political promise.”

But Senator Dianne Feinstein, Democrat of California, the chairwoman of the Intelligence Committee, praised Mr. Obama’s move, noting that the two had been “cleared for transfer years ago” and arguing that at an annual cost of $2.7 million to house each detainee, “it is in the national security interests of the United States to transfer these detainees to their home countries.”

Mr. Lietzau, who will leave his position next month, was traveling to Guantánamo on Friday and could not be reached for comment. In an e-mail he sent to his staff at the Pentagon on Thursday, he said he had accepted a job as vice president and deputy general counsel for PAE, a government services company.