Motivation: 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-or distance-assisted threading methods utilize only the residue pairs predicted to be spatially close for template selection and alignment, ignoring the neighborhood effect induced by the interacting pairs. Results: We present a new distance-based covariational threading method called DisCovER by effectively integrating information from distance maps and their topological network neighborhood. Our method first selects a subset of templates using standard profile-based threading to perform distancebased query-template alignment, and then iteratively improves the sensitivity of the alignment through double dynamic programming by incorporating topological network similarity terms induced by distance-derived inter-residue interaction network to account for the neighborhood effect. Multiple largescale benchmarking results on query proteins classified in current literature as hard threading targets show that our method greatly outperforms not only the traditional threading methods including SparkX, HHpred, CNFpred, MUSTER, PPAS, and pGenThreader; but also the state-of-the-art contact-assisted threading approaches such as CEthreader, map_align, EigenTHREADER, and CATHER. As threading gets harder and harder by the exclusion of more and more structurally similar templates, the performance of our method gets better and better compared to the contact-assisted approaches CEthreader, map_align, and EigenTHREADER. At one of the hardest threading scenarios, the average performance of DisCovER is much better than the reported average accuracy of the only other distance-based threading method DeepThreader, which is not publicly available. Controlled experiments reveal that integration of distance information significantly improves threading template selection and alignment and is one of the key factors behind the improved performance of DisCovER.