Age-related changes in the human brain functioning crucially affect the motor system, causing increased reaction time, low ability to control and execute movements, difficulties in learning new motor skills. The lifestyle and lowered daily activity of elderly adults, along with the deficit of motor and cognitive brain functions, might lead to the developed ambidexterity, i.e., the loss of dominant limb advances. Despite the broad knowledge about the changes in cortical activity directly related to the motor execution, less is known about age-related differences in the motor initiation phase. We hypothesize that the latter strongly influences the behavioral characteristics, such as reaction time, the accuracy of motor performance, etc. Here, we compare the neuronal processes underlying the motor initiation phase preceding fine motor task execution between elderly and young subjects. Based on the results of the whole-scalp sensor-level electroencephalography (EEG) analysis, we demonstrate that the age-related slowing down in the motor initiation before the dominant hand movements is accompanied by the increased theta activation within sensorimotor area and reconfiguration of the theta-band functional connectivity in elderly adults.