The ongoing pandemic of coronavirus disease 2019 (COVID-19) has led to global health and healthcare crisis, apart from the tremendous socioeconomic effects. One of the significant challenges in this crisis is to identify and monitor the COVID-19 patients quickly and efficiently to facilitate timely decisions for their treatment, monitoring, and management. Research efforts are on to develop less time-consuming methods to replace or to supplement RT-PCR-based methods. The present study is aimed at creating efficient deep learning models, trained with chest X-ray images, for rapid screening of COVID-19 patients. We used publicly available PA chest X-ray images of adult COVID-19 patients for the development of Artificial Intelligence (AI)-based classification models for COVID-19 and other major infectious diseases. To increase the dataset size and develop generalized models, we performed 25 different types of augmentations on the original images. Furthermore, we utilized the transfer learning approach for the training and testing of the classification models. The combination of two best-performing models (each trained on 286 images, rotated through 120° or 140° angle) displayed the highest prediction accuracy for normal, COVID-19, non-COVID-19, pneumonia, and tuberculosis images. AI-based classification models trained through the transfer learning approach can efficiently classify the chest X-ray images representing studied diseases. Our method is more efficient than previously published methods. It is one step ahead towards the implementation of AI-based methods for classification problems in biomedical imaging related to COVID-19.