The World Health Organization and other institutions are considering Artificial Intelligence (AI) as a technology that can potentially address some health system gaps, especially the reduction of global health inequalities in low- and middle-income countries (LMICs). However, because most AI-based health applications are developed and implemented in high-income countries, their use in LMICs contexts is recent and there is a lack of robust local evaluations to guide decision-making in low-resource settings. After discussing the potential benefits as well as the risks and challenges raised by AI-based health care, we propose five building blocks to guide the development and implementation of more responsible, sustainable, and inclusive AI health care technologies in LMICs.