Reliable and real-time propagation loss modeling play a significant role in the efficient planning, development, and optimization of macrocellular communication networks in a given terrain. Thus, the need to adapt or tune an existing model to enhance its signal prediction accuracy in a specified terrain becomes imperative. In this paper, we proposed and applied a non-linear square regression method based on the Levenberg-Marquart (LM) algorithm to adapt and improve the empirical propagation loss estimation accuracy of the Egli model for two major cities in Nigeria. A comprehensive propagation loss measurement acquired over Long Term Evolution (LTE) mobile broadband networks operating at 2630 MHz for four different cities was collected using TEMS investigation tools to achieve the Egli model adaption. Results indicate that the adapted Egli model displays a high estimation accuracy over the Gauss-Newton (GN) algorithm leveraging the non-linear regression method employed to benchmark the propagation loss estimation. Using six standard statistical indicators, the adapted Egli model displayed lower estimation errors than the classical Egli model across the tested locations in the two cities investigated. Finally, the LM-adapted Egli model was compared with extensive measurements from another eNodeB in Port Harcourt different from the initial four eNodeBs investigated. The results indicate that the adapted model is suitable for deployment in related macrocellular environments.