It has been long proposed that, if all the terrestrial planets form within a tiny ring of solid material at around 1 AU, the concentrated mass-distance distribution of the current system can be reproduced. Recent planetesimal formation models also support this idea. In this study, we revisit the ring model by performing a number of high-resolution N-body simulations for 10 Myr of a ring of self-interacting planetesimals, with various radial distributions of the gas disc. We found that even if all the planetesimals form at ∼1 AU in a minimum mass solar nebula-like disc, the system tends to spread radially as accretion proceeds, resulting in a system of planetary embryos lacking mass-concentration at ∼1 AU. Modifying the surface density of the gas disc into a concave shape with a peak at ∼1 AU helps to maintain mass concentrated at ∼1 AU and solve the radial dispersion problem. We further propose that such a disc should be short lived (≤ 1 Myr) and with a shallower radial gradient in the innermost region (< 1 AU) than previously proposed to prevent a too-rapid growth of Earth. Future studies should extend to ∼100 Myr the most promising simulations and address in a self-consistent manner the evolution of the asteroid belt and its role in the formation of the terrestrial planets.