Fundamental rights impact assessments are an important tool for deployers of high-risk AI systems to identify the specific risks, to estimate the likelihood and severity of adverse impacts on fundamental rights, and to put in place the measures necessary to address them. They allow for an assessment to be made at an early stage, before the AI system is put into use, that enables risks to be addressed before they eventuate, including through adjustments to design. Deployers that are bodies governed by public law, or private operators providing public services, and deployers operating certain high-risk AI systems should therefore be required to conduct an assessment of the impact on fundamental rights of the deployment of the AI system in a specific context, before putting the system into use. Such assessment should identify the specific risks to the individuals or groups of individuals likely to be affected, specify the appropriate measures to address those risks, and ensure that appropriate oversight measures are in place at all times during the operation of the AI system. In order to use the AI system in a specific context, market surveillance authorities should be able to assess whether or not the fundamental rights impact assessment meets its requirements and to request additional information or measures where necessary.