Climate change will drive migration both within and across nations' borders, requiring some temporary and permanent resettlement. Despite the relative novelty of – and growing need for – climate-driven migration, it is unknown whether or how support for climate refugees' plight differs to other refugees. We examine attitudes of people living in the United States (N = 1765) towards refugee policy that experimentally differs in three respects: the type of refugees (international climate refugees, internal climate refugees, or refugees of war), the length of their stay (permanent or temporary), and their numbers (capped or increasing annually). While specific discussion about climate refugee policy cites fears of ‘opening the floodgates’, we found no evidence that people were reluctant to support climate refugees when their numbers were going to increase each year compared to when they would remain capped. Instead, ratings did not depend on refugee numbers or refugee permanence. None of these factors interacted, indicating that resistance to migration is contingent only on the group: Proposals to support international climate refugees were supported less than proposals to support internal climate refugees or refugees of war. Responses to a question asking which countries participants expected international climate refugees to relocate from suggests a wide variety of expected origins, and these geographic origins may shape ratings of support and perceived threat to the economy and culture if refugees resettle in the United States. Overall, our findings highlight the greater support and sympathy afforded to groups already living in the United States.