Precision measurements by the Alpha Magnetic Spectrometer (AMS) on the International Space Station of the deuteron (𝐷) flux are presented. The measurements are based on $21×10^6$ 𝐷 nuclei in the rigidity range from 1.9 to 21 GV collected from May 2011 to April 2021. We observe that over the entire rigidity range the 𝐷 flux exhibits nearly identical time variations with the 𝑝, $^{3}\textrm{He}$, and $^{4}\textrm{He}$ fluxes. Above 4.5 GV, the $D/^{4}\textrm{He}$ flux ratio is time independent and its rigidity dependence is well described by a single power law $\propto R ^{\Delta}$ with $\Delta _{D/^{4}\textrm{He}} = −0.108 \pm 0.005$. This is in contrast with the $^3\textrm{He}/^4\textrm{He}$ flux ratio for which we find $\Delta _{^{3}\textrm{He}/^{4}\textrm{He}}=−0.289 \pm 0.003$. Above ∼13  GV we find a nearly identical rigidity dependence of the 𝐷 and 𝑝 fluxes with a 𝐷/𝑝 flux ratio of $0.027 \pm 0.001$. These unexpected observations indicate that cosmic deuterons have a sizable primarylike component. With a method independent of cosmic ray propagation, we obtain the primary component of the 𝐷 flux equal to $9.4 \pm 0.5\%$ of the $^{4}\textrm{He}$ flux and the secondary component of the 𝐷 flux equal to $58 \pm 5\%$ of the $^{3}\textrm{He}$ flux.