Ensuring the provision of accessible, affordable, and high-quality public services to all individuals aligns with one of the paramount aims of the United Nations’ Sustainable Development Goals (SDGs). In the face of escalating urbanization and a dwindling rural populace in China, reconstructing rural settlements to enhance public service accessibility has become a fundamental strategy for achieving the SDGs in rural areas. However, few studies have examined the optimal methods for rural settlement reconstruction that ensure accessible and equitable public services while considering multiple existing facilities and service provisions. This paper focuses on rural settlement reconstruction in the context of the SDGs, employing an inverted MCLP-CC (maximal coverage location problem for complementary coverage) model to identify optimal rural settlements and a rank-based method for their relocation. Conducted in Changyuan, a county-level city in Henan Province, China, this study observed significant enhancements in both accessibility and equity following rural settlement reconstruction by utilizing the MH3SFCA (modified Huff 3-step floating catchment area) and the spatial Lorenz curve method. Remarkably, these improvements were achieved without the addition of new facilities, with the accessibility increasing by 44.21%, 4.97%, and 3.11%; Gini coefficients decreasing by 19.53%, 1.64%, and 3.18%; Ricci-Schutz coefficients decreasing by 21.09%, 2.09%, and 4.33% for educational, medical, and cultural and sports facilities, respectively. It indicated that rural settlement reconstruction can bolster the accessibility and equity of public services by leveraging existing facilities. This paper provides a new framework for stakeholders to better reconstruct rural settlements and promote sustainable development in rural areas in China.