In oral communication, especially public speaking, it is essential to speak at a speed that is appropriate for the situation. However, speech control requires substantial training. Although several speech-training systems that provide automated feedback on users' speech quality or behavior have been developed, users are still required to consciously control their ways of speaking to improve their speech. This study proposes a speech-supporting system that enables users to speak at a pace close to the target rate with minimum conscious adjustment. Because auditory feedback on the speaker's voice with a short delay disturbs speaking, we used auditory feedback with continuously varying delay times to slow the speaker's speech rate when speaking fast. We implemented a prototype and conducted a user study with ten speakers to confirm the effects on the speech style of the speaker during public speaking. The results show that the proposed system can slow the speech rate when the user speaks quickly without instructing the speaker on how to respond to auditory feedback. The findings also suggest that the proposed system causes less discomfort to the speaker than delayed auditory feedback with a constant delay.