1. A speech processing apparatus comprising: a speech receiving unit that receives input speech; a speech processing unit that obtains a text character string from the input speech; an analyzing unit that performs a morphological analysis of the text character string; a generating unit that divides the text character string into components in units of division that are previously decided and composed of at least one of the morphemes, and generates partial character string candidates including part of the components; a first output unit that outputs the partial character string candidates to a display unit; and a selection receiving unit that receives a partial character string selected from the partial character string candidates.