According to APS, the official Algerian news agency, the 25-year-old man, whom the Independent is not naming, is "alive and well, and not under threat in any way." The National Observatory for Human Rights (ONDH), has also stated that reports that he died in Algerian police custody are "groundless" and "manifestly a crude manoeuvre intended to blacken the reputation of the Algerian authorities."
But the British Refugee Council, which has conducted its own investigation into the case, said that neither statement allayed its concerns.
The man, who had served in the Algerian police, was arrested and released on his arrival back in the country but then rearrested, according to information received by the council and other sources.
He was believed to have met his death during this second detention.
An ONDH news release confirms that he was arrested on his arrival at Algiers airport on 27 April and "released the same day and returned to his family home in Algiers".
A spokeswoman for the Refugee Council said nothing in the two statements had caused it to change its view of the case.
"The ONDH has admitted that he was detained on arrival but has added nothing about him being detained the second time, during which we believe he was killed."
The ONDH claims in its release that the man "suspected his former comrades in the London detention centre of having fabricated the whole story in order to cast a pall of Algerian-British relations and our country's reputation at a time when it is preparing for important elections."
But in an indication that the agency has not itself sought to interview the man, it adds that ONDH "has learnt" that the man has made himself available for any subsequent inquiry.