Phonon scattering in metals is one of the most fundamental processes in materials science. However, understanding such processes has remained challenging and requires detailed information on interactions between phonons and electrons. We use an ultrafast electron diffuse scattering technique to resolve the nonequilibrium phonon dynamics in femtosecond-laser-excited tungsten in both time and momentum. We determine transient populations of phonon modes which show strong momentum dependence initiated by electron-phonon coupling. For phonons near Brillouin zone border, we observe a transient rise in their population on a timescale of approximately 1 picosecond driven by the strong electron-phonon coupling, followed by a slow decay on a timescale of approximately 8 picosecond governed by the weaker phonon-phonon relaxation process. We find that the exceptional harmonicity of tungsten is needed for isolating the two processes, resulting in long-lived nonequilibrium phonons in a pure metal. Our finding highlights that electron-phonon scattering can be the determinant factor in the phonon thermal transport of metals.