Somalia's al-Shabab fighters claim to have executed a captured Kenyan soldier and have repeated threats to kill five other hostages.
The claim of the al-Qaeda-linked group, made on Friday, could not be independently verified.
"While the mujahedeen have executed the serving KDF [Kenya Defence Force] soldier, there is still a chance of securing the release of the remaining five prisoners," al-Shabab said in a statement.
Last month al-Shabab issued a February 14 deadline ordering Kenya - whose troops are fighting the anti-government group seeking to impose Islamic law inside Somalia - to release "all Muslim prisoners held on so-called terrorism charges in Kenya".
Al-Shababn fighters, who have previously released videos of Kenyan civil servants they have kidnapped, have said they will execute five hostages within three days unless the Kenyan government gave in to their demands.
News of the alleged execution came as AU troops and government forces seized on Thursday the towns of Janalle, Aw Dhigle and Barire, about 80km southwest of the capital Mogadishu, the latest al-Shabab bases to fall.
Kenya has been hit by a spate of attacks including hand grenade and bombs since it invaded southern Somalia in late 2011 to attack al-Shabab bases, following a string of kidnappings inside Kenya blamed on the armed group.
Many of the attacks in Kenya - including hand grenade blasts in the capital Nairobi - are blamed on al-Shabab supporters or Kenyan sympathisers, although al-Shabab has not claimed the attacks themselves.
But the once powerful al-Shabab are on the defensive inside Somalia, having fled a string of key towns in the face of a 17,000-strong African Union force - which includes Kenyan troops - which is fighting alongside Somali soldiers.
Ethiopian troops are also battling al-Shabab in the southwest of Somalia.
Even so, al-Shabab remains a potent threat, still controlling rural areas as well as carrying out guerrilla attacks in areas apparently under government control.