Resting-state brain activities have been extensively investigated to understand the macro-scale network architecture of the human brain using non-invasive imaging methods such as fMRI, EEG and MEG. Previous studies revealed a mechanistic origin of the resting-state networks (RSNs) using the connectome dynamics modeling approach, where the neural mass dynamics model constrained by the structural connectivity is simulated to replicate the resting-state networks measured with fMRI and/or fast synchronization transitions with EEG/MEG. However, there is still little understanding of the relationship between the slow fluctuations measured with fMRI and the fast synchronization transitions with EEG/MEG. In this study, as a first step toward evaluating experimental evidence of resting state activity at two different time scales but in a unified way, we investigate the connectome dynamics models that simultaneously explain resting-state functional connectivity (rsFC) and EEG microstates. Here, we introduce empirical rsFC and microstates as evaluation criteria of simulated neuronal dynamics obtained by the Larter-Breakspear model in one cortical region connected with those in other cortical regions based on structural connectivity. We optimized the global coupling strength and the local gain parameter (variance of the excitatory threshold) of the simulated neuronal dynamics by fitting both rsFC and microstate spatial patterns to those of experimental ones. As a result, we found that simulated neuronal dynamics in a narrow optimal parameter range simultaneously reproduced empirical rsFC and microstates. Two parameter groups had different inter-regional interdependence. One type of dynamics was synchronized across the whole brain region, and the other type was synchronized between brain regions with strong structural connectivity. Our results demonstrate that a bottom-up approach, which extends the single neuronal dynamics model based on empirical observations into the neural mass dynamics model and integrates structural connectivity, effectively reveals both macroscopic fast and slow resting-state network dynamics.