Channels on the Martian surface suggest that Mars had an early, relatively thick atmosphere. If the atmosphere was thick enough for water to be stable at the surface, CO₂ in the atmosphere would have been fixed as carbonates on a relatively short time scale, previously estimated to be 1 bar every 10⁷ years. This loss must have been offset by some replenishment mechanism to account for the numerous valley networks in the oldest surviving terrains. Impacts could have released CO₂ into the atmosphere by burial, by shock-induced release during impact events, and by addition of carbon to Mars from the impacting bolides. Depending on the relationship between the transient cavity diameter and the diameter of the resulting crater, burial rates as a result of impact gardening at the end of heavy bombardment are estimated to range from 20 to 45 m/10⁶ years, on the assumption that cratering rates in Mars were similar to those of the Nectarian Period on the Moon. At these rates 0.1-0.2 bar of CO₂ could have been released every 107 years as a result of burial to depths where dissociation temperatures of carbonates were reached. Modeling of large impacts suggests that an additional 0.01 to 0.02 bar of CO₂ could have been released every 10⁷ years during the actual impacts. In the unlikely event that all the impacting material was composed of carbonaceous chondrites, a further 0.3 bar of CO₂ could have been added to the atmosphere every 10⁷ years by oxidation of meteoritic carbon. Even when supplemented by the volcanically induced release of CO₂, these release rates are barely sufficient to sustain an early atmosphere if water were continuously present at the surface. The results suggest that water may have been only intermittently present on the surface early in the planet's history.