Al-Qaida in the Islamic Maghreb (AQIM) said Britain should abandon its plans to deport Qatada and would have to "bear the consequences" if it went ahead.
It said it would release Stephen Malcolm, who has British and South African dual citizenship, if Qatada was sent to one of the Arab spring countries – Egypt, Tunisia, Libya or Yemen. Malcolm is one of nine Europeans seized in Mali and Niger since September 2010.
In an unverified statement posted on an Islamist website, AQIM said: "The initiative to the British government is to release its citizen Stephen Malcolm, who also has South African nationality, if it deports Abu Qatada to one of the Arab spring countries. If Britain ignores this offer it will bear the consequences of handing Abu Qatada to the Jordanian government."
The home secretary, Theresa May, is trying to deport Qatada to Jordan, where he faces a retrial on terror charges. He is being held at Belmarsh prison, in south-east London, pending a bail application.
His lawyers have applied to the grand chamber of the European court of human rights in Strasbourg in an attempt to block the deportation, and it may be months before a final decision is made.
The appeal provoked a heated dispute in parliament over whether a three-month deadline to deport Qatada with the necessary assurances from Jordan expired on the night of 16 or 17 April.
Qatada could be freed within a matter of weeks if Mr Justice Mitting, president of the special immigration appeals commision (Siac), rules that Qatada's deportation is not imminent.
The Home Office said it could not comment on the AQIM statement. Successive British governments have adopted a policy of never accepting deals offered by kidnappers.
AQIM has been increasing its influence in west Africa, raising a "worrying aspect of an arc of regional instability encompassing the whole Sahara-Sahel strip and extending through to east Africa", according to a recent report by the Royal United Services Institute.
