The novel human coronavirus disease COVID-19 has become the fifth documented pandemic since the 1918 flu pandemic. COVID-19 was first reported in Wuhan, China, and subsequently spread worldwide. Almost all of the countries of the world are facing this natural challenge. We present forecasting models to estimate and predict COVID-19 outbreak in Asia Pacific countries, particularly Pakistan, Afghanistan, India, and Bangladesh. We have utilized the latest deep learning techniques such as Long Short Term Memory networks (LSTM), Recurrent Neural Network (RNN), and Gated Recurrent Units (GRU) to quantify the intensity of pandemic for the near future. We consider the time variable and data non-linearity when employing neural networks. Each model’s salient features have been evaluated to foresee the number of COVID-19 cases in the next 10 days. The forecasting performance of employed deep learning models shown up to July 01, 2020, is more than 90% accurate, which shows the reliability of the proposed study. We hope that the present comparative analysis will provide an accurate picture of pandemic spread to the government officials so that they can take appropriate mitigation measures.