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Coronaviruses constitute a family of viruses that gives rise to respiratory diseases. As COVID-19 is highly contagious, early diagnosis of COVID-19 is crucial for an effective treatment strategy. However, the RT-PCR test which is considered to be a gold standard in the diagnosis of COVID-19 suffers from a high false-negative rate. Chest X-ray (CXR) image analysis has emerged as a feasible and effective diagnostic technique towards this objective. In this work, we propose the COVID-19 classification problem as a three-class classification problem to distinguish between COVID-19, normal, and pneumonia classes. We propose a three-stage framework, named COV-ELM. Stage one deals with preprocessing and transformation while stage two deals with feature extraction. These extracted features are passed as an input to the ELM at the third stage, resulting in the identification of COVID-19. The choice of ELM in this work has been motivated by its faster convergence, better generalization capability, and shorter training time in comparison to the conventional gradient-based learning algorithms. As bigger and diverse datasets become available, ELM can be quickly retrained as compared to its gradient-based competitor models. The proposed model achieved a macro average F1-score of 0.95 and the overall sensitivity of ${0.94 \pm 0.02} at a 95% confidence interval. When compared to state-of-the-art machine learning algorithms, the COV-ELM is found to outperform its competitors in this three-class classification scenario. Further, LIME has been integrated with the proposed COV-ELM model to generate annotated CXR images. The annotations are based on the superpixels that have contributed to distinguish between the different classes. It was observed that the superpixels correspond to the regions of the human lungs that are clinically observed in COVID-19 and Pneumonia cases.