The duality between the localized and itinerant nature of magnetism in 5f-electron systems has been a long-standing puzzle. Here, we report inelastic neutron scattering measurements, which reveal both local and itinerant aspects of magnetism in a single-crystalline system of UPt_{2}Si_{2}. In the antiferromagnetic state, we observe a broad continuum of diffuse magnetic scattering with a resonancelike gap of ≈7 meV and the surprising absence of coherent spin waves, suggestive of itinerant magnetism. While the gap closes above the Néel temperature, strong dynamic spin correlations persist to a high temperature. Nevertheless, the size and temperature dependence of the total magnetic spectral weight can be well described by a local moment with J=4. Furthermore, polarized neutron measurements reveal that the magnetic fluctuations are mostly transverse, with little or none of the longitudinal component expected for itinerant moments. These results suggest that a dual description of local and itinerant magnetism is required to understand UPt_{2}Si_{2} and, by extension, other 5f systems, in general.