Qassem Askar Jebrane, Yemen's ambassador to Algeria, said the Armed Islamic Group (GIA) made the offer in a message handed to him and another diplomat, Omani ambassador Hillal al-Siyabi, when their abductors let them go on Friday.
'The letter says the armed groups are prepared to stop the campaign of assassinating foreigners if the leadership liberates Abdelhak Layada,' Mr Jebrane said in an interview. 'We have transmitted this message to the Algerian authorities.'
Layada, one of the founders of the GIA, was arrested in Morocco in June last year and sentenced to death by an Algerian court.
Islamic fundamentalists have been fighting the secular government since the military cancelled elections in January 1992 an Islamic coalition had been poised to win.