The electroreduction of carbon dioxide (CO2RR) to valuable chemicals is a promising avenue for the storage of intermittent renewable electricity. Renewable methane, obtained via CO2RR using renewable electricity as energy input, has the potential to serve as a carbon-neutral fuel or chemical feedstock, and it is of particular interest in view of the well-established infrastructure for its storage, distribution, and utilization. However, CO2RR to methane still suffers from low selectivity at commercially relevant current densities (>100 mA cm(-2)). Density functional theory calculations herein reveal that lowering *CO2 coverage on the Cu surface decreases the coverage of the *CO intermediate, and then this favors the protonation of *CO to *CHO, a key intermediate for methane generation, compared to the competing step, C-C coupling. We therefore pursue an experimental strategy wherein we control local CO2 availability on a Cu catalyst by tuning the concentration of CO2 in the gas stream and regulate the reaction rate through the current density. We achieve as a result a methane Faradaic efficiency (FE) of (48 +/- 2)% with a partial current density of (108 +/- 5) mA cm(-2) and a methane cathodic energy efficiency of 20% using a dilute CO2 gas stream. We report stable methane electrosynthesis for 22 h. These findings offer routes to produce methane with high FE and high conversion rate in CO2RR and also make direct use of dilute CO2 feedstocks.