Droughts have a substantial impact on water supplies, agriculture, and ecosystems worldwide. Agricultural sustainability and production in the Mekong Delta of Vietnam are being jeopardized by droughts caused by climate change. Conventional forecasting methods frequently struggle to comprehend the intricate dynamics of meteorological occurrences connected to drought, necessitating the use of sophisticated prediction techniques. This study assesses the effectiveness of various statistical models (ARIMA), machine learning, and deep learning models (Gradient Boosting, XGBoost, RNN, and LSTM) in forecasting the SPEI over different time periods (1, 3, 6, and 12 months) across six prediction intervals. The models were developed and evaluated using data from 11 meteorological stations spanning from 1985 to 2022. These models incorporated various climatic variables, including precipitation, temperature, humidity, potential evapotranspiration (PET), Southern Oscillation Index (SOI) Anomaly, and sea surface temperature in the NINO4 region (SST_NINO4). The results demonstrate that XGBoost and LSTM models exhibit outstanding performance, showcasing lower error metrics and higher R² values compared to Gradient Boosting and RNN. The performance of the model fluctuated depending on the forecast step, with error metrics often increasing with longer prediction horizons. The use of climatic indices improved the accuracy of the model. These findings are consistent with earlier research on drought episodes in the Mekong Delta and support studies from other areas that show the effectiveness of advanced modeling tools for predicting droughts. The work emphasizes the capacity of machine learning and deep learning models to enhance the precision of drought forecasting, which is vital for efficient water resource management and agricultural planning in places prone to drought.