Fidel Castro, Cuba's former president and leader of the Communist revolution, has died aged 90.
In their message to the government and people of Cuba, the leaders expressed sadness over his death.
President Mulatu said Castro was a friend to Ethiopia which helped the later in its struggle to defend its territorial integrity.
The strong tie between the two countries, established during the leadership of Castro, has a special value in the history of both countries, he added.
In his message, Prime Minister Hailemariam said generations will remember Castro because of his support to Ethiopia during those challenging times, referring the Ethio-Somalia war.
Cuba has supported Ethiopia during the Ethio-Somalia War, a military offensive by Somalia between July 1977 and March 1978 over the Ogaden region in Ethiopian.