COVID-19 was declared a global pandemic by the World Health Organisation (WHO) on 11th March 2020. Many researchers have, in the past, attempted to predict a COVID outbreak and its effect. Some have regarded time-series variables as primary factors which can affect the onset of infectious diseases like influenza and severe acute respiratory syndrome (SARS). In this study, we have used public datasets provided by the European Centre for Disease Prevention and Control for developing a prediction model for the spread of the COVID-19 outbreak to and throughout Malaysia, Morocco and Saudi Arabia. We have made use of certain effective deep learning (DL) models for this purpose. We assessed some specific major features for predicting the trend of the existing COVID-19 outbreak in these three countries. In this study, we also proposed a DL approach that includes recurrent neural network (RNN) and long short-term memory (LSTM) networks for predicting the probable numbers of COVID-19 cases. The LSTM models showed a 98.58% precision accuracy while the RNN models showed a 93.45% precision accuracy. Also, this study compared the number of coronavirus cases and the number of resulting deaths in Malaysia, Morocco and Saudi Arabia. Thereafter, we predicted the number of confirmed COVID-19 cases and deaths for a subsequent seven days. In this study, we presented their predictions using the data that was available up to December 3rd, 2020.