Background: As middle-income countries strive to achieve the Sustainable Development Goals (SDGs), it remains unclear to what degree expanding primary care coverage can help achieve those goals and reduce within-country inequalities in mortality. We estimated the potential impact of primary care expansion on cause-specific mortality in the 15 largest Brazilian cities. Methods: We obtained hazard ratios of death by cause and by demographic group, from a national administrative database linked to the Estrategia de Saude da Familia (Family Health Strategy, FHS) electronic health and death records among 1.2 million residents of Rio de Janeiro (2010-2016). We incorporated these hazard ratios into a microsimulation to estimate the impact of changing primary care coverage. Findings: Increased FHS coverage would be expected to reduce inequalities in mortality among cities (from 2.8 to 2.4 deaths per 1,000 between the highest- and lowest-mortality city, given a 40 percentage point increase in coverage), between welfare recipients and non-recipients (from 1.3 to 1.0 deaths per 1,000), and among race/ethnic groups (between Black and White Brazilians from 1.0 to 0.8 deaths per 1,000). A 40 percentage point increase in coverage would be insufficient to reach SDG targets --reducing premature mortality from non-communicable diseases by 20% (versus the target of 33%), and communicable diseases by 15% (versus 100%). Interpretation: Primary care coverage may be critically beneficial to reducing within-country health inequalities, but reaching SDG targets will likely require coordination between primary care and other sectors. Funding Statement: This work was supported by a grant from the Health Systems Research Initiative with funding from the Foreign, Commonwealth and Development Office, the UK Medical Research Council and Wellcome Trust, in collaboration with the UK Economic and Social Research Council (grant no. MR/P014593/1).DR acknowledges support from the Spanish Ministry of Science and Innovation through the “Centro de Excelencia Severo Ochoa 2019-2023” Program (CEX2018- 000806-S), and support from the Generalitat de Catalunya through the CERCA Program. Declaration of Interests: None. Ethics Approval Statement: Approval for this study was obtained from the Brazilian National Commission for Ethics in Research (Comissao Nacional de Etica em Pesquisa [CONEP]; number 2.689.528) and Imperial College London’s Ethical Comittee.