Identifying the core microbiome structure of a metaorganism can be used to monitor the impact of a perturbation against it and the changes in its stability (i.e., dysbiosis), resistance, and resilience. The core‐microbiome interaction regulates holobiont health and homeostasis and is an indicator of the resilience of the whole community. This study determined the exclusive and shared core microbiome taxa of two reef‐building coral species (Pocillopora damicornis and P. verrucosa), as well as the surrounding seawater and sediment, in six coral communities along the Northeastern tropical Pacific region. We also analysed the putative metabolic functions of the most abundant OTUs of these core microbiomes and evaluated the influence of anthropogenic stressors (i.e., tourism, fishery, eutrophication, among others) on core microbiome composition. Bacterial diversity was assessed by sequencing the V4 region of the 16S rRNA. The bacterial families Planctomycetaceae, Oceanospirillaceae, and Moraxellaceae presented the highest relative abundances in corals samples, while Flavobacteriaceae and Rhodobacteraceae dominated in seawater samples. In the sediment samples, Pseudoalteromonadaceae, Oxalobacteraceae, Moraxellaceae, and Pseudonocardiaceae had the highest representation. The core microbiomes of the two coral species, seawater, and sediment, shared 571 OTUs. The P. damicornis core microbiome varied between sites with low and moderately‐high anthropogenic stressors. The core microbiomes of both coral species showed an increase in the relative abundance of the families Planctomycetaceae and Pseudomonadaceae in the sites with moderate‐high anthropogenic stressors, associated with higher values of ammonium, chlorophyll a, and extinction coefficient. In contrast, the core microbiome of P. verrucosa, seawater, and sediments did not vary between sites with different anthropogenic stress conditions. Aerobic chemoheterotrophy was the metabolic function with the highest occurrence in all substrates' core microbiomes, followed by ureolysis and photoautotrophy.