This article deals with the problem of argumentative communication in the form of a public speech at the Intercultural level from the standpoint of the Cognito-lingua cultural methodology of foreign language education; the subject of a special study is the question of the leading method of teaching public argumentative speech; the process of teaching public speech is presented as an integration of presentation and argumentative components in the context of Intercultural communicative competence; and special attention is paid to strategies and tactics of speech expression of public argumentative speech.