Speech is the most important signal in our auditory environment, and the processing of speech is highly dependent on context. However, it is unknown how contextual demands influence the neural encoding of speech. Here, we examine the context dependence of auditory cortical mechanisms for speech encoding at the level of the representation of fundamental acoustic features (spectrotemporal modulations) using model-based functional magnetic resonance imaging. We found that the performance of different tasks on identical speech sounds leads to neural enhancement of the acoustic features in the stimuli that are critically relevant to task performance. These task effects were observed at the earliest stages of auditory cortical processing, in line with interactive accounts of speech processing. Our work provides important insights into the mechanisms that underlie the processing of contextually relevant acoustic information within our rich and dynamic auditory environment.