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Threading a query protein sequence onto a library of weakly homologous structural templates remains challenging, even when sequence‐based predicted contact or distance information is used. Contact‐assisted or distance‐assisted threading methods utilize only the spatial proximity of the interacting residue pairs for template selection and alignment, ignoring their orientation. Moreover, existing threading methods fail to consider the neighborhood effect induced by the query–template alignment. We present a new distance‐ and orientation‐based covariational threading method called DisCovER by effectively integrating information from inter‐residue distance and orientation along with the topological network neighborhood of a query–template alignment. Our method first selects a subset of templates using standard profile‐based threading coupled with topological network similarity terms to account for the neighborhood effect and subsequently performs distance‐ and orientation‐based query–template alignment using an iterative double dynamic programming framework. Multiple large‐scale benchmarking results on query proteins classified as weakly homologous from the continuous automated model evaluation experiment and from the current literature show that our method outperforms several existing state‐of‐the‐art threading approaches, and that the integration of the neighborhood effect with the inter‐residue distance and orientation information synergistically contributes to the improved performance of DisCovER. DisCovER is freely available athttps://github.com/Bhattacharya-Lab/DisCovER.