Many motor tasks in everyday life, such as driving and cooking, involve a combination of discrete and rhythmic movements. While an increasing number of studies have identified discrete and rhythmic movements as fundamental components in complex motor control, the dynamic interactions between them remain elusive. This study aimed to quantify changes in kinematics when ongoing rhythmic movement of the right arm is perturbed by either rhythmic (RI) or discrete initiation (DI) of the left arm. Fourteen young adults (12 right-handed, 2 ambidextrous) performed bimanual forearm rotations on a horizontal plane under two conditions, i.e., RI and DI. We analyzed the change of instantaneous phase progression. Results showed that the perturbed magnitude and direction in the ongoing right arm were dependent on the relative phase between the two arms at the initiation of the left arm in both DI and RI. When observing the phase progression over the duration of the movement of discrete reaching, perturbations in the DI condition were comparable to those in the RI condition. However, over an extended duration beyond the discrete movement time, perturbations in the DI condition were significantly larger than those in the RI condition. The results suggest that, while the bimanual interaction appears consistent across the two types of movement, termination rather than initiation of discrete movements may engage distinct motor control processes compared to rhythmic movements.