Motivation: Electronic Health Records (EHR) represent a comprehensive resource of a patient's medical history. EHR are essential for utilizing advanced technologies such as deep learning (DL), enabling healthcare providers to analyze extensive data, extract valuable insights, and make precise and data-driven clinical decisions. DL methods such as Recurrent Neural Networks (RNN) have been utilized to analyze EHR to model disease progression and predict diagnosis. However, these methods do not address some inherent irregularities in EHR data such as irregular time intervals between clinical visits. Furthermore, most DL models are not interpretable. In this study, we propose two interpretable DL architectures based on RNN, namely Time-Aware RNN (TA-RNN) and TA-RNN-Autoencoder (TA-RNN-AE) to predict patient's clinical outcome in EHR at next visit and multiple visits ahead, respectively. To mitigate the impact of irregular time intervals, we propose incorporating time embedding of the elapsed times between visits. For interpretability, we propose employing a dual-level attention mechanism that operates between visits and features within each visit. Results: The results of the experiments conducted on Alzheimer's Disease Neuroimaging Initiative (ADNI) and National Alzheimer's Coordinating Center (NACC) datasets indicated superior performance of proposed models for predicting Alzheimer's Disease (AD) compared to state-of-the-art and baseline approaches based on F2 and sensitivity. Additionally, TA-RNN showed superior performance on Medical Information Mart for Intensive Care (MIMIC-III) dataset for mortality prediction. In our ablation study, we observed enhanced predictive performance by incorporating time embedding and attention mechanisms. Finally, investigating attention weights helped identify influential visits and features in predictions.