Goal: Because of the outbreak of coronavirus infection, healthcare systems are faced with the lack of medical professionals. We present a system for the differential diagnosis of coronavirus disease, based on deep learning techniques, which can be implemented in clinics. Methods: A recurrent network with a convolutional neural network as an encoder and an attention mechanism is used. A database of about 3000 records of coughing was collected. The data was collected through the Acoustery mobile application in hospitals in Russia, Belarus, and Kazakhstan from April 2020 to October 2020. Results: The model classification accuracy reaches 85%. Values of precision and recall metrics are 78.5% and 73%. Conclusions: We reached satisfactory results in solving the problem. The proposed model is already being tested by doctors to understand the ways of improvement. Other architectures should be considered that use a larger training sample and all available patient information.