This paper considers the Euclidean traveling salesman problem (a nondeterministic polynomial hard combinatorial optimization problem). The main goal of this work is to extend the applicability of polynomial algorithms for special cases of Euclidean traveling salesman problem such as problems with vertices lying on a convex hull to more general point configurations. For this purpose, the pairwise comparison method is used. The result of the work is a new heuristic algorithm with a guaranteed absolute error, which consists of three stages. At the first stage, the set of points is divided into subsets forming nested convex polygons. At the second stage, subproblems for each polygon are solved as a special case of the Euclidean traveling salesman problem with linear complexity. At the third stage, the solutions of the subproblems are combined into a single route. The theoretical part of the work is devoted to estimating the error of the proposed algorithm. It has been proven that the absolute error of the solution depends on the number of convex polygons and the distances between them. It is shown that as the distance between the polygons increases, the error tends to zero. Additionally, the concept of the ε-neighborhood of a convex polygon is introduced (an area in which points can be added to the bypass based on the nearest distance to the vertices of the polygon without violating the optimality of the bypass). The operation of the algorithm and the validity of the statements were verified through numerical experiments using examples from the Traveling Salesman Problem Library. The results confirmed that as the distance between convex hulls increases, the relative error decreases. It is also shown that an increase in the number of convex hulls leads to an increase in error, which requires minimizing their number in practical applications. In conclusion, directions for further research are noted, including the search for guaranteed error estimates, parameter optimization, and generalization of the method to multidimensional Euclidean spaces.