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 million 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, ${}^3$He , and ${}^4$He fluxes. Above 4.5 GV, the 𝐷/${}^4$He flux ratio is time independent and its rigidity dependence is well described by a single power law ∝𝑅$^\Delta$ with $Δ_{𝐷/{}^4\text{He}}$ =−0.108±0.005. This is in contrast with the ${}^3$He/${}^4$He flux ratio for which we find $Δ_{{}^3\text{He}/{}^4\text{He}}$ =−0.289±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 ±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 ±0.5% of the ${}^4$He flux and the secondary component of the 𝐷 flux equal to 58 ±5% of the ${}^3$He flux.