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A change in the global climate on early Mars is suspected from the geologic evidence of warmer wetter conditions that prevailed during the Noachian but stands in contrast to the dry and cold conditions observed currently. However, the timing and evolution of this climatic change represents a gap in our understanding of the history of Mars. Here, we document the time-dependence of the crater obliteration rates on Mars that decreased continuously between 3.8 Ga and 3 Ga. Our results indicate that the erosion responsible for crater modification and obliteration declined gradually through the Noachian and into the Hesperian periods. These results suggest that the climatic conditions also changed gradually and the amount of water available on the surface of Mars slowly decreased over time.