Background The ambitious development agenda of the Sustainable Development Goals (SDGs) requires substantial investments across several sectors, including for SDG 3 (healthy lives and wellbeing). No estimates of the additional resources needed to strengthen comprehensive health service delivery towards the attainment of SDG 3 and universal health coverage in low-income and middle-income countries have been published. Methods We developed a framework for health systems strengthening, within which population-level and individual-level health service coverage is gradually scaled up over time. We developed projections for 67 low-income and middle-income countries from 2016 to 2030, representing 95% of the total population in low-income and middle-income countries. We considered four service delivery platforms, and modelled two scenarios with differing levels of ambition: a progress scenario, in which countries’ advancement towards global targets is constrained by their health system’s assumed absorptive capacity, and an ambitious scenario, in which most countries attain the global targets. We estimated the associated costs and health effects, including reduced prevalence of illness, lives saved, and increases in life expectancy. We projected available funding by country and year, taking into account economic growth and anticipated allocation towards the health sector, to allow for an analysis of affordability and financial sustainability.