Substantial progress towards understanding neural computation has been made by studying the dynamical systems that govern neural population activity. Because dynamical models make predictions about the temporal evolution of neural states, perturbations of neural activity are a powerful tool to evaluate and refine these models. Here, using electrodes and Neuropixels in the motor cortices of macaques engaged in a reaching task, we probed how local population dynamics are affected by two perturbation modalities: optogenetic excitation and electrical intracortical microstimulation (ICMS). Both stimulation modalities drove strong, transient changes in nearby neurons' firing rates, causing a large displacement of the neural state. To study the interaction of perturbation with task-related activity, we stimulated at one of multiple timepoints on randomly interleaved trials. We developed a latent variable model similar to GPFA, that incorporates an additive, low-rank perturbation term and a rectified-Poisson observation model. This approach revealed that optogenetic stimulation was adequately described as additive, simply translating the neural state. While neural activity during ICMS also contained this additive component, neural states across different reach conditions contracted together during stimulation. Strikingly, the amount of this stimulation-induced contraction correlated with the magnitude of the evoked displacement of hand velocity. Our findings reveal a difference in engagement of cortical dynamics under optogenetic excitation and ICMS. While large additive transients dominate stimulation responses of both modalities, the additive transient alone was insufficient to produce kinematic effects. We hypothesize that additive perturbations may produce strong behavioral effects when specifically targeted to the low-dimensional subspaces that govern population dynamics and behavior. Perturbations that engage neural dynamics nonlinearly—in this case, by contracting neural states—can readily impact population activity and behavior without special targeting approaches. Ultimately, combining perturbations with simultaneous observation of neural responses will yield new insights into the mechanisms of neural computation and inform effective therapeutic interventions.