Water allocation regimes that adjudicate between competing uses are in many countries under pressure to adapt to increasing demands, climate‐driven shortages, expectations for equity of access, as well as societal changes in values and priorities. International authorities expound standards for national allocation regimes that include robust processes for addressing the needs of ‘new entrants' and for varying existing entitlements within sustainable limits. The claims of Indigenous peoples to water represents a newly recognised set of rights and interests that will test the ability of allocation regimes to address the global water governance goal of equity. No study has sought to identify public attitudes or willingness to pay for a fairer allocation of water rights between Indigenous and non‐Indigenous people. We surveyed households from the jurisdictions of Australia's Murray‐Darling Basin, a region undergoing a historic government‐led recovery of water, and found that 69.2% of respondents support the principle of reallocating a small amount of water from irrigators to Aboriginal people via the water market. Using contingent valuation, we estimated households are willing to pay A$21.78 in a one‐off levy. The aggregate value calculated for households in the basin's jurisdictions was A$74.5 million, which is almost double a recent government commitment to fund the acquisition of entitlements for Aboriginal nations of this basin. Results varied by state of residency and affinity with environmental groups. An information treatment that presented narrative accounts from Aboriginal people influenced the results. Insights from this study can inform water reallocation processes.