1. A speech processing apparatus comprising: a rule storing unit that stores therein a rule that correlates causes of errors in speech recognition, responding methods each of which is used when an error has occurred during the speech recognition, and responding users each of whom is one of a first user and a second user, the first user being a user that inputs a speech and the second user being a user that does not input a speech; an input receiving unit that receives an input of a speech; a recognizing unit that recognizes the received speech; a detecting unit that detects a cause of an error that has occurred during the recognition of the speech; a method selecting unit that selects one of the responding methods that is correlated with the detected cause of the error from the rule storing unit; a user selecting unit that selects one of the responding users that is correlated with the detected cause of the error from the rule storing unit; and an executing unit that executes the response to the selected responding user by the selected responding method.