Since the first case of COVID-19 was reported in December 2019, many studies have been carried out on artificial intelligence for the rapid diagnosis of the disease to support health services. Therefore, in this study, we present a powerful approach to detect COVID-19 and COVID-19 findings from computed tomography images using pre-trained models using two different datasets. COVID-19, influenza A (H1N1) pneumonia, bacterial pneumonia and healthy lung image classes were used in the first dataset. Consolidation, crazy-paving pattern, ground-glass opacity, ground-glass opacity and consolidation, ground-glass opacity and nodule classes were used in the second dataset. The study consists of four steps. In the first two steps, distinctive features were extracted from the final layers of the pre-trained ShuffleNet, GoogLeNet and MobileNetV2 models trained with the datasets. In the next steps, the most relevant features were selected from the models using the Sine–Cosine optimization algorithm. Then, the hyperparameters of the Support Vector Machines were optimized with the Bayesian optimization algorithm and used to reclassify the feature subset that achieved the highest accuracy in the third step. The overall accuracy obtained for the first and second datasets is 99.46% and 99.82%, respectively. Finally, the performance of the results visualized with Occlusion Sensitivity Maps was compared with Gradient-weighted class activation mapping. The approach proposed in this paper outperformed other methods in detecting COVID-19 from multiclass viral pneumonia. Moreover, detecting the stages of COVID-19 in the lungs was an innovative and successful approach.