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Aim: The continental island system comprising Sakhalin, Hokkaido and the southern Kuril Islands (SHSK) in northeastern Asia serves as one of the southernmost habitats for many boreal and arctic organisms, with colonization via land bridges formed during glacial periods. To understand the impacts of past land‐bridge formation under Quaternary climate changes across SHSK, we investigated the demographic history of forest‐dwelling marten species. Location: Sakhalin, Hokkaido and the southern Kuril Islands in northeastern Asia. Taxon: Sable, Martes zibellina (Carnivora, Mustelidae). Methods: We employed multiplexed inter‐simple sequence repeat genotyping by sequencing (MIG‐seq) to obtain genome‐wide single nucleotide polymorphisms (SNPs). We tested possible scenarios of colonization and diversification for SHSK sables using several population genetics approaches including clustering analysis, population tree estimation and approximate Bayesian computation modelling. We also examined haplotype diversity for the mitochondrial ND2 gene. Results: The genetic diversity of the island populations and their affinity for continental populations were found to be higher in the order Sakhalin > Hokkaido > Iturup in both nuclear SNP and mitochondrial DNA analyses. Demographic analyses indicated that the sable migrated repeatedly from the continent, particularly to the neighbouring Sakhalin Island. However, only an earlier colonized lineage has persisted on marginal Iturup Island since the Middle Pleistocene. The stronger effects of repeated migrations and/or isolation influenced by the distance to the continent have shaped the contemporary genetic diversity and differentiation of sable populations in SHSK. Main Conclusions: Genome‐wide and comprehensive sampling approaches demonstrated that the forest‐dwelling sable had long‐term persistence with partial admixture of multiple lineages in SHSK, suggesting the existence of forest corridors and refugia on the islands during the last several glacial periods. The SHSK system of continental islands is valuable for understanding the impacts of Quaternary climate changes on the genetic diversity and evolutionary histories of boreal organisms. [ABSTRACT FROM AUTHOR]