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Background Ultra-deep next-generation sequencing of circulating tumor DNA (ctDNA) holds great promise as a tool for the early detection of cancer and for monitoring disease progression and therapeutic responses. However, the low abundance of ctDNA in the bloodstream coupled with technical errors introduced during library construction and sequencing complicates mutation detection. Results To achieve high accuracy of variant calling via better distinguishing low-frequency ctDNA mutations from background errors, we introduce TNER (Tri-Nucleotide Error Reducer), a novel background error suppression method that provides a robust estimation of background noise to reduce sequencing errors. The results on both simulated data and real data from healthy subjects demonstrate that the proposed algorithm consistently outperforms a current, state-of-the-art, position-specific error polishing model, particularly when the sample size of healthy subjects is small. Conclusions TNER significantly enhances the specificity of downstream ctDNA mutation detection without sacrificing sensitivity. The tool is publicly available at https://github.com/ctDNA/TNER. Electronic supplementary material The online version of this article (10.1186/s12859-018-2428-3) contains supplementary material, which is available to authorized users.