The traveling salesman problem (TSP) is a fundamental NP-hard optimization problem. Over the past decades, traditional heuristic methods have achieved substantial success in solving TSP, yet their performance, particularly for large-scale instances, remains to be further improved. The advancement of deep learning technologies over the past decade has driven a growing number of attempts to solve TSP by leveraging neural guidance. However, these efforts predominantly focus on small-scale TSP instances, with limited improvements in solving performance for large-scale instances, revealing persistent scalability challenges. This work presents UNiCS, a novel unified neural-guided cascaded solver for solving large-scale TSP instances. UNiCS comprises a local search (LS) phase and a population-based search (PBS) phase, both guided by a learning component called unified neural guidance (UNG). Specifically, UNG guides solution generation across both phases and determines appropriate phase transition timing to effectively combine the complementary strengths of LS and PBS. While trained only on simple distributions with relatively small-scale TSP instances, UNiCS generalizes effectively to challenging TSP benchmarks containing much larger instances (10,000-71,009 nodes) with diverse node distributions entirely unseen during training. Experimental results on the large-scale TSP instances demonstrate that UNiCS consistently outperforms state-of-the-art methods, with its advantage remaining consistent across various runtime budgets.