Attorney Robert Kirsch said he had pressed the Pentagon and State Department, along with the Algerian Embassy in Washington, to avoid the men's "imminent" repatriation set to take place as early as this weekend.
Without confirming when and where a detainee transfer may take place, a Pentagon spokesman said: "We carefully ensure that every transfer we carry out is consistent with the US government's humane treatment policy and standards."
"Consistent with the Convention Against Torture and our own commitment to human rights, the United States is firm in its commitment to not transfer detainees to countries where we believe they would face torture," spokesman Todd Breasseale told AFP yesterday.
Belkacem Bensayah and Djamel Ameziane's protests over their pending transfer, however, is complicating Obama's efforts to meet his vow to shutter the US detention center in Cuba, where 164 "war on terror" suspects still linger nearly 12 years after it was opened.
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US lawmakers are currently debating whether to lift restrictions on detainee transfers.
Bensayah and Ameziane have long been opposed to returning to their homeland, the only country authorized by US law to accept its nationals detained at Guantanamo, according to Kirsch, who represents Bensayah.
Ameziane's lead attorney Wells Dixon said that he "cannot confirm or deny" reports that his client is about to be transferred.
"But I can confirm as a general matter that Djamel fears persecution in Algeria and does not want to return there," Dixon told AFP via e-mail.
"He would like to be resettled in Europe or Canada, where he has viable resettlement opportunities."
Bensayah is demanding to be returned to Bosnia, where he was arrested in 2002 and where his wife and daughters live.
"Bensayah believes Muslim extremists will expect him to sympathize with them, only because he was held at Guantanamo. He fears that they will attack or perhaps kill him when they learn he does not support them.