The conductance of one-dimensional interacting electron systems is calculated in a manner similar to Landauer's argument for non-interacting systems. Unlike in previous studies in which the Kubo formula was used, the conductance is directly evaluated as the ratio of current $J$ to the chemical potential difference $\Delta \mu$ between right-going and left-going particles. It is shown that both $J$ and $\Delta \mu$ are renormalized by electron-electron (e-e) interactions, but their ratio, the conductance, is not renormalized at all if the e-e interactions are the only scattering mechanism. It is also shown that nonequilibrium current fluctuation at low frequency is absent in such a case. These conclusions are drawn for both Fermi liquids (in which quasi-particles are accompanied with the backflow) and Tomonaga-Luttinger liquids.