We demonstrate use of iteratively pruned deep learning model ensembles for detecting pulmonary manifestation of COVID-19 with chest X-rays. This disease is caused by the novel Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) virus, also known as the novel Coronavirus (2019-nCoV). A custom convolutional neural network and a selection of ImageNet pretrained models are trained and evaluated at patient-level on publicly available CXR collections to learn modality-specific feature representations. The learned knowledge is transferred and fine-tuned to improve performance and generalization in the related task of classifying CXRs as normal, showing bacterial pneumonia, or COVID-19-viral abnormalities. The best performing models are iteratively pruned to reduce complexity and improve memory efficiency. The predictions of the best-performing pruned models are combined through different ensemble strategies to improve classification performance. Empirical evaluations demonstrate that the weighted average of the best-performing pruned models significantly improves performance resulting in an accuracy of 99.01% and area under the curve of 0.9972 in detecting COVID-19 findings on CXRs. The combined use of modality-specific knowledge transfer, iterative model pruning, and ensemble learning resulted in improved predictions. We expect that this model can be quickly adopted for COVID-19 screening using chest radiographs.