An Al-Qaeda-linked Islamist group based in northern Mali warned Algeria of deadly reprisals on Friday after Algerian officials rejected a hostage swap, a statement released by the group said.

The so-called Movement for Oneness and Jihad in West Africa (MUJAO) is one of several emergent Islamist groups that seized control of northern Mali after a disastrous March coup in the capital Bamako.

Earlier this month, three armed Islamists were arrested by Algerian security forces in a special operation near the southern Algerian town of Ghardaia, according to official Algerian news service APS.

The detainees belong to Al-Qaeda in the Islamic Maghreb (AQIM), to which MUJAO is allied, MUJAO said in a statement sent to AFP on Friday.

MUJAO said it has asked the Algerian government "to free our brothers" in exchange for MUJAO freeing one of the Algerian hostages.

"The Algerian government rejected the offer. Consequently, Algeria will be subject to all the consequences of this refusal," the statement said.

MUJAO has claimed the April 5 kidnapping of seven Algerian diplomats from a consulate in Gao, in central Mali. Three of the hostages have been freed so far.

MUJAO said among those arrested in Algeria as Abd Arrahmane Abu Ishak, who heads AQIM's legal commission.

"We are giving an ultimatum of less than five days, starting from now, to save the life of the (Algerian) hostage," MUJAO official Abu Walid Sahraoui said in the statement.

"We intend to treat the Algerian authorities firmly. We will defend our mujahadeen brothers ... until the fall of the military regime in Algeria."

Islamists swept across northern Mali after a March 22 coup carried out by troops protesting the government's response to the Islamist presence in the vast desert north.

Several towns have since been placed under hardline sharia law, which has seen the carrying out of extreme punishments including the stoning to death of an unmarried couple.