The intensity and frequency of extreme event occurrence, especially floods, have significantly increased owing to climate change and anthropogenic activities. To effectively minimize the worst effects of flooding, reliable streamflow forecasts at increased lead times are crucial. However, in most cases, the accuracy of the model deteriorates as the lead time increases. Further, the propagation of uncertainty in the forecast greatly reduces the reliability of the forecast. Therefore, besides improving the accuracy, uncertainty quantification of the streamflow forecast is also important to increase the confidence of the model for further decision-making. This study proposes a novel physics-aware machine learning-based modeling framework to forecast up to 7 days ahead of streamflow keeping the objective of preventing the deterioration in model accuracy and simultaneously quantifying the uncertainty. The framework is developed by coupling the process-based HBV hydrological model with the Bayesian-based Particle filter to estimate the streamflow prediction interval. Subsequently, the ensemble mean computed from the PI of streamflow was used as input into the machine learning algorithm of Random Forest. The model was tested on the Beas and Sunkoshi river basin of India and Nepal, through several statistical performance and uncertainty indices. The framework achieved NSE of 0.94 and 0.98 in calibration and 0.95 and 0.99 in validation for the 7-day ahead streamflow forecast of the Beas and Sunkoshi river basin respectively, with insignificant deterioration in accuracy. Overall, the proposed dynamic modeling framework could be a potential tool to forecasts streamflow at increased lead times, without significant deterioration in accuracy.