Pursuing Equity in Mental Health Act This bill sets out activities and modifies existing programs to address racial and ethnic mental health disparities. Specifically, the Department of Health and Human Services (HHS) must implement a strategy for promoting behavioral and mental health and reducing stigma associated with mental health conditions and substance use disorder among racial and ethnic minority groups. HHS must consult with appropriate advocacy groups and behavioral health organizations on this strategy. Additionally, HHS must seek to contract with the National Academies of Sciences, Engineering, and Medicine for a study on research gaps related to mental health disparities among racial and ethnic minority groups. Modifications to existing programs include (1) permitting HHS to prioritize health care facilities that serve a high proportion of racial and ethnic minority groups when awarding grants for integrating physical and behavioral health care, and (2) extending the authorization for the grants from FY2027 through FY2029. The bill also permits the use of funds available through the Minority Fellowship Program for developing best practices or core competencies to address mental health disparities in curricula for training social workers, psychologists, and other behavioral health professionals. (This program supports the education and training of minority students who are studying for advanced degrees in a mental or behavioral health profession.)