The novel COVID-19 is a global pandemic disease overgrowing worldwide. Computer-aided screening tools with greater sensitivity is imperative for disease diagnosis and prognosis as early as possible. It also can be a helpful tool in triage for testing and clinical supervision of COVID-19 patients. However, designing such an automated tool from non-invasive radiographic images is challenging as many manually annotated datasets are not publicly available yet, which is the essential core requirement of supervised learning schemes. This article proposes a 3D Convolutional Neural Network (CNN)-based classification approach considering both the inter- and intra-slice spatial voxel information. The proposed system is trained in an end-to-end manner on the 3D patches from the whole volumetric CT images to enlarge the number of training samples, performing the ablation studies on patch size determination. We integrate progressive resizing, segmentation, augmentations, and class-rebalancing to our 3D network. The segmentation is a critical prerequisite step for COVID-19 diagnosis enabling the classifier to learn prominent lung features while excluding the outer lung regions of the CT scans. We evaluate all the extensive experiments on a publicly available dataset, named MosMed, having binary- and multi-class chest CT image partitions. Our experimental results are very encouraging, yielding areas under the ROC curve of 0.914 and 0.893 for the binary- and multi-class tasks, respectively, applying 5-fold cross-validations. Our methods promising results delegate it as a favorable aiding tool for clinical practitioners and radiologists to assess COVID-19.