The aim of the study was to develop a computerized method for distinguishing COVID-19-affected cases from cases of pneumonia. This task continues to be a real challenge in the practice of diagnosing COVID-19 disease. In the study, a new approach was proposed, using a comprehensive set of diagnostic information (CSDI) including, among other things, medical history, demographic data, signs and symptoms of the disease, and laboratory results. These data have the advantage of being much more reliable compared with data based on a single source of information, such as radiological imaging. On this basis, a comprehensive process of building predictive models was carried out, including such steps as data preprocessing, feature selection, training, and evaluation of classification models. During the study, 9 different methods for feature selection were used, while the grid search method and 12 popular classification algorithms were employed to build classification models. The most effective model achieved a classification accuracy (ACC) of 85%, a sensitivity (TPR) equal to 83%, and a specificity (TNR) of 88%. The model was built using the random forest method with 15 features selected using the recursive feature elimination selection method. The results provide an opportunity to build a computer system to assist the physician in the diagnosis of the COVID-19 disease.