Climate change alters the global distribution of leishmaniasis vector sandfly species. However, the possible effect of altering environmental factors on sandfly species varies by species and area. The aim of this study was to project the future potential effect of climate change on the Western Asian occurrence of the sandfly vector species Phlebotomus papatasi and Phlebotomus sergenti and the parasites Leishmania major and Leishmania tropica for 2041–2060 and 2081–2100 compared to their modelled climatic suitability patterns in the reference period 1970–2000. The model results suggest that by 2041–2060 and 2081–2100, in the coastal areas of the Levantine countries and the mid-elevation regions of Western Iran and Southeast Turkey, the climatic suitability of all the studied species is predicted to increase. In contrast, the model results suggest the decline of the populations of the studied vectors as well as the disappearance of the parasites in Iraq, North Saudi Arabia, Kuwait, and the inland regions of Western Asian countries. Considering the present-day population density patterns, it can be said that although in large regions of the region, the climatic suitability values are predicted to decrease, the populated Levantine regions seem to be at risk of climate change-facilitated increase in cutaneous leishmaniasis in the second half of the twenty-first century. The model results suggest that climate change will especially increase the climatic suitability of Leishmania tropica in the Levantine region in the late twenty-first century.