The density peaks clustering (DPC) algorithm has gained significant attention in various fields due to its simplicity and effectiveness. However, its performance is constrained by the local density calculation method and the selection of the cutoff distance $d_c$, which is a parameter primarily dependent on global data distribution, while neglecting local characteristics. Additionally, the one-step assignment strategy in DPC is prone to chain errors caused by single-point misassignment, adversely affecting clustering performance. To address these limitations, this paper proposes the interactive neighbors similarity-based density peaks clustering (INSDPC) algorithm. The algorithm introduces an interactive neighbors similarity measure that combines the information of interactive neighbors and shared neighbors to redefine local density. Furthermore, a two-step assignment strategy, leveraging interactive neighbors similarity and neighborhood information, is designed to avoid further errors when a point is incorrectly assigned. Experimental results on synthetic and real-world datasets demonstrate that INSDPC improves cluster centers identification and enhances clustering precision.