The present invention relates to a press-type composite internally and externally threaded portion forming system. In this case, the press-type composite internally and externally threaded portion forming system includes an expansion-type collet core unit (10) and a contraction-type collet core unit (20) as its principal components so that internally and externally threaded portions are formed by means of a press method in a composite manner in such a way that the expansion forming force of the expansion-type collet core unit (10) and the contraction forming force of the contraction-type collet core unit (20) simultaneously act on the inner and outer circumferential surfaces of a workpiece in opposite directions.