Incháustegui then became a representative of the Cuban government at the Headquarters of the United Nations. During the Cuban missile crisis in October 1962, he described the Soviet missiles as defensive and that the naval blockade imposed by the Kennedy administration was a military act. From 1963 to 1968, he headed the international organizations department of the Ministerio del Comercio Exterior (MINCEX), (Cuban Foreign Trade Ministry) and represented the Cuban government at numerous international conferences, such as conducting negotiations at the meetings of the International Coffee Organization in London. From 1969 to 1970, he represented the Cuban government at the United Nations Office at Geneva.