Resting tremor in Parkinson's disease is characterized by considerable variability: tremor affects some patients but not others, and its amplitude typically fluctuates. Previous research focused primarily on identifying mechanisms that produce tremor, showing an important role for the basal ganglia and cerebello-thalamo-cortical circuit. What has been relatively ignored are mechanisms involved in suppressing tremor. For instance, patients can reduce their tremor by making voluntary movements or by exerting conscious effort. Here, we aimed to distinguish between brain mechanisms that contribute positively or negatively to spontaneous fluctuations in Parkinson's tremor. We leveraged a large sample of 119 tremulous Parkinson patients with concurrent accelerometry-fMRI. Frame-by-frame fluctuations in accelerometry-derived tremor power, measured per patient, were used to localize tremor-related brain activations and deactivations at a group level. Amplitude-related coupling between tremor-positive and tremor-negative brain networks was examined further using physio-physiological interaction analyses. Lastly, whole-brain multiple regression analyses were used to test the association between tremor-related activity and clinically assessed tremor severity. Tremor-related activations were found in a lateralized network consisting of contralateral (to tremor) sensorimotor cortex, ventrolateral thalamus, posterior putamen, and cerebellum (ipsilateral lobule V, vermis, and bilateral Crus I/II); activity in this network correlated positively with tremor severity. Tremor-related deactivations encompassed a bilateral "anti-tremor" network, including dorsal premotor cortex, pre-supplementary motor area, somatosensory cortex, posterior parietal cortex, and insula; activity in this network correlated negatively with tremor severity. During low versus high tremor episodes, functional connectivity between the anti-tremor and tremor-positive networks increased. This suggests that the anti-tremor network makes a relevant contribution to modulating tremor amplitude by connecting to the cerebello-thalamo-cortical circuit in a tremor-dependent manner. We conclude that spontaneous fluctuations in Parkinson's tremor amplitude are associated with interactions between a tremor-producing cerebello-thalamo-cortical circuit and a novel antagonistic anti-tremor network. Future intervention studies may investigate whether strengthening of the anti-tremor network leads to a reduction in tremor, as a potential basis for new therapies.