This paper discusses iterative approximations of solution of nonlinear ill-posed operator equation \(F(x)=y\). Here the right hand side \(y\) is given approximately by \(y^\delta\) and \(\|y^\delta -y\|\leq\delta\), the operator \(F\) is a continuous and Fréchet differentiable. The solution of this equation does not depend continuously on the right hand side \(y\). The author considers the following iteratively regularized Gauss-Newton method \[ x_{k+1}^\delta=x_k^\delta-(\alpha_k I+F'(x_k^\delta)^*F'(x_k^\delta))^{-1} (F'(x_k^\delta)^*(F(x_k^\delta)^*(F(x_k^\delta)-y^\delta) +\alpha_k(x_k^\delta-x_0))), \] where \(x_0^\delta=x_0\) is an initial guess of the exact solution \(x^+\) of the noise-free equation and \(\{\alpha_k\}\) is a decreasing sequence of positive numbers used to regularize the interation process. A stopping rule is designed for selecting the approximation \(x_{k_\delta}^\delta\) such that \[ \|x_{k_\delta}^\delta - x^+\|\leq C \inf\biggl\{ \|x_k-x^+\|+\frac{\delta}{\sqrt{\alpha_k}}~:~k=0,1,\ldots\biggr\} . \] Here \(C\) is constant independent of \(\delta\) and \(x_k\) is the iterative approximation of the solution \(x^+\). Numerical examples illustrate estimation of parameters.