Speech Emotion Recognition (SER), the extraction of emotional features with the appropriate classification from speech signals, has recently received attention for its emerging social applications. Emotional intensity (e.g., Normal, Strong) for a particular emotional expression (e.g., Sad, Angry) has a crucial influence on social activities. A person with intense sadness or anger may fall into severe disruptive action, eventually triggering a suicidal or devastating act. However, existing Deep Learning (DL)-based SER models only consider the categorization of emotion, ignoring the respective emotional intensity, despite its utmost importance. In this study, a novel scheme for Recognition of Emotion with Intensity from Speech (REIS) is developed using the DL model by integrating three speech signal transformation methods, namely Mel-frequency Cepstral Coefficient (MFCC), Short-time Fourier Transform (STFT), and Chroma STFT. The integrated 3D form of transformed features from three individual methods is fed into the DL model. Moreover, under the proposed REIS, both the single and cascaded frameworks with DL models are investigated. A DL model consists of a 3D Convolutional Neural Network (CNN), Time Distribution Flatten (TDF) layer, and Bidirectional Long Short-term Memory (Bi-LSTM) network. The 3D CNN block extracts convolved features from 3D transformed speech features. The convolved features were flattened through the TDF layer and fed into Bi-LSTM to classify emotion with intensity in a single DL framework. The 3D transformed feature is first classified into emotion categories in the cascaded DL framework using a DL model. Then, using a different DL model, the intensity level of the identified categories is determined. The proposed REIS has been evaluated on the Ryerson Audio-Visual Database of Emotional Speech and Song (RAVDESS) benchmark dataset, and the cascaded DL framework is found to be better than the single DL framework. The proposed REIS method has shown remarkable recognition accuracy, outperforming related existing methods.