"The lives of millions of human beings who inhabit the planet depend on what a few people think, believe and decide," he said in a 50-minute speech at the solemn event in the Karl Marx theatre.
"A smaller group of countries that monopolises these weapons boast the exclusive right to produce and develop them."
"We have the right to denounce, to pressure and to demand changes and an end to this ridiculous and absurd situation that has turned us into hostages," he said.
Castro also criticised the Free Trade Area of the Americas, a scheme championed by the United States to tear down trade barriers throughout the western hemisphere.
The plan does not include Cuba, which is isolated as the only Communist nation in the Americas.
Castro led rebels into the eastern city of Santiago on 1 January 1959. Former president Fulgencio Batista fled to the Dominican Republic on the same day, and Castro has ruled since then.