Several critical tasks in biology such as detecting tandem repeats from error-prone long reads and reconstructing circular RNAs from rolling circle long-reads data, require solving a fundamental computational problem: given a sequence containing an unknown number of mutated copies of an unknown repeat unit, reconstruct the original unit. While several methods exist for this problem, they often exhibit low accuracy when the repeat unit length increases or the number of copies is low. Furthermore, methods capable of handling highly mutated sequences remain scarce, highlighting significant need for improvement. We introduce EquiRep, a tool for accurate detection of tandem repeats from error-prone sequences. By evaluating using simulated and real datasets we show that EquiRep consistently outperforms state-of-the-art methods. EquiRep is robust to sequencing errors, and is able to make better predictions for long units and low frequencies, underscoring its broad usability. EquiRep is freely available at https://github.com/Shao-Group/EquiRep . The full version of this manuscript is available at https://doi.org/10.1101/2024.11.05.621953 .