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Abstract Background Advancement in screening tools accessible to the general population for the early detection of Alzheimer’s disease (AD) and prediction of its progression is essential for achieving timely therapeutic interventions and conducting decentralized clinical trials. This study delves into the application of Machine Learning (ML) techniques by leveraging paralinguistic features extracted directly from a brief spontaneous speech (SS) protocol. We aimed to explore the capability of ML techniques to discriminate between different degrees of cognitive impairment based on SS. Furthermore, for the first time, this study investigates the relationship between paralinguistic features from SS and cognitive function within the AD spectrum. Methods Physical-acoustic features were extracted from voice recordings of patients evaluated in a memory unit who underwent a SS protocol. We implemented several ML models evaluated via cross-validation to identify individuals without cognitive impairment (subjective cognitive decline, SCD), with mild cognitive impairment (MCI), and with dementia due to AD (ADD). In addition, we established models capable of predicting cognitive domain performance based on a comprehensive neuropsychological battery from Fundació Ace (NBACE) using SS-derived information. Results The results of this study showed that, based on a paralinguistic analysis of sound, it is possible to identify individuals with ADD (F1 = 0.92) and MCI (F1 = 0.84). Furthermore, our models, based on physical acoustic information, exhibited correlations greater than 0.5 for predicting the cognitive domains of attention, memory, executive functions, language, and visuospatial ability. Conclusions In this study, we show the potential of a brief and cost-effective SS protocol in distinguishing between different degrees of cognitive impairment and forecasting performance in cognitive domains commonly affected within the AD spectrum. Our results demonstrate a high correspondence with protocols traditionally used to assess cognitive function. Overall, it opens up novel prospects for developing screening tools and remote disease monitoring.