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The newly discovered Coronavirus Disease 2019 (COVID-19) has been globally spreading and causing hundreds of thousands of deaths around the world as of its first emergence in late 2019. The rapid outbreak of this disease has overwhelmed health care infrastructures and arises the need to allocate medical equipment and resources more efficiently. The early diagnosis of this disease will lead to the rapid separation of COVID-19 and non-COVID cases, which will be helpful for health care authorities to optimize resource allocation plans and early prevention of the disease. In this regard, a growing number of studies are investigating the capability of deep learning for early diagnosis of COVID-19. Computed tomography (CT) scans have shown distinctive features and higher sensitivity compared to other diagnostic tests, in particular the current gold standard, i.e., the Reverse Transcription Polymerase Chain Reaction (RT-PCR) test. Current deep learning-based algorithms are mainly developed based on Convolutional Neural Networks (CNNs) to identify COVID-19 pneumonia cases. CNNs, however, require extensive data augmentation and large datasets to identify detailed spatial relations between image instances. Furthermore, existing algorithms utilizing CT scans, either extend slice-level predictions to patient-level ones using a simple thresholding mechanism or rely on a sophisticated infection segmentation to identify the disease. In this paper, we propose a two-stage fully automated CT-based framework for identification of COVID-19 positive cases referred to as the "COVID-FACT". COVID-FACT utilizes Capsule Networks, as its main building blocks and is, therefore, capable of capturing spatial information. In particular, to make the proposed COVID-FACT independent from sophisticated segmentations of the area of infection, slices demonstrating infection are detected at the first stage and the second stage is responsible for classifying patients into COVID and non-COVID cases. COVID-FACT detects slices with infection, and identifies positive COVID-19 cases using an in-house CT scan dataset, containing COVID-19, community acquired pneumonia, and normal cases. Based on our experiments, COVID-FACT achieves an accuracy of $90.82\text{\%}$ , a sensitivity of $94.55\text{\%}$ , a specificity of $86.04\text{\%}$ , and an Area Under the Curve (AUC) of 0.98, while depending on far less supervision and annotation, in comparison to its counterparts.