One of the possible modifications of the Newton method for solving nonlinear system of equations is the inexact Newton method. The basic idea underlining this type of method is to approximate solution of Newton equation by applying linear iterative method. Many results for both local and global convergence are known for this method. This paper focuses on a wider class of methods, which are the result of preconditioning of the Newton equation by some nonsingular matrix $A$. By introducing the relaxation parameter $t_k$, we achieve, under suitable assumptions, global convergence. Mutual influence of parameters $t_k$ and $\eta_k$ also be discussed.