The non‐native pet trade contributes directly to species invasions, thereby threatening wildlife. Biological invasions influence environmental change, resulting in species extinctions and biodiversity loss. To mitigate the pet trade invasion risk, interventions are required to prevent trade in non‐native animals with high invasion potential, impulse or ill‐informed purchases of non‐native pets by individuals who may release these animals, and the deliberate release of non‐native animals by pet owners. Interventions are also required to prevent the establishment of non‐native animals that have been released by pet owners (e.g., euthanasia). The successful implementation of these interventions depends on the support of pet owners and the public in the form of political support for, and compliance with, interventions. In 2017–2018, using both mail and online surveys, we measured the support of 1,171 members of the public and 550 owners of non‐native pets in Florida, USA, for 7 different interventions to mitigate the pet trade invasion risk, and we investigated determinants of this support. We found that individuals' support for interventions depended on their concern related to the invasion risks associated with the pet trade, trust in government to manage the pet trade, perceptions of how effective interventions would be in mitigating the pet trade invasion risk, and demographic characteristics. Support for interventions differed across pet owners and the public. Educating pet owners about the traits and cost of care for non‐native animals and providing them with options to relinquish unwanted pets may reduce the pet trade invasion risk. Engaging the pet trade in the design of interventions to mitigate invasion risks is likely important to attain voluntary compliance with these interventions. The effectiveness of interventions also depends on enforcement by agencies. Implementing interventions that effectively reduce the pet trade invasion risk is important to protect native and endangered wildlife.