The goal of this study is to develop an automated algorithm to quantify background electroencephalography (EEG) dynamics in term neonates with hypoxic ischemic encephalopathy. The recorded EEG signal is adaptively segmented and the segments with low amplitudes are detected. Next, depending on the spatial distribution of the low-amplitude segments, the first part of the algorithm detects (dynamic) interburst intervals (dIBIs) and performs well on the relatively artifact-free EEG periods and well-defined burst-suppression EEG periods. However, on testing the algorithm on EEG recordings of more than 48 h per neonate, a significant number of misclassified and dubious detections were encountered. Therefore, as the next step, we applied machine learning classifiers to differentiate between definite dIBI detections and misclassified ones. The developed algorithm achieved a true positive detection rate of 98%, 97%, 88%, and 95% for four duration-related dIBI groups that we subsequently defined. We benchmarked our algorithm with an expert diagnostic interpretation of EEG periods (1 h long) and demonstrated its effectiveness in clinical practice. We show that the detection algorithm effectively discriminates challenging cases encountered within mild and moderate background abnormalities. The dIBI detection algorithm improves identification of neonates with good clinical outcome as compared to the classification based on the classical burst-suppression interburst interval.