Abstract The default mode network (DMN), the salience network (SN), and the central executive network (CEN) could be considered as the core resting-state brain networks (RSN) due to their involvement in a wide range of cognitive tasks. Despite the large body of knowledge relating to their regional spontaneous activity (RSA) and functional connectivity (FC) of these networks, less is known about the influence of task-associated activity on these parameters and on the interaction between these three networks. We have investigated the effects of the visual-oddball paradigm on three fMRI measures (amplitude of low-frequency fluctuations for RSA, regional homogeneity for local FC, and degree centrality for global FC) in these three core RSN networks. A rest-task-rest paradigm was used and the RSNs were identified using independent component analysis (ICA) on the resting-state data. We found that the task-related brain activity induced different patterns of significant changes within the three RS networks. Most changes were strongly associated with the task performance. Furthermore, the task-activity significantly increased the inter-network correlations between the SN and CEN as well as between the DMN and CEN, but not between the DMN and SN. A significant dynamical change in RSA, alongside local and global FC within the three core resting-state networks following a simple cognitive activity may be an expression of the distinct involvement of these networks in the performance of the task and their various outcomes.