This paper proposes some classical estimators of the population mean using the data on two auxiliary variables under a two-phase sampling scheme with subsampling the nonrespondents. This study considers the scenario in which nonresponse affects the study and first auxiliary variables but not the supporting auxiliary variable. The expression for the bias and means square error of the proposed estimator has been derived up to the first order of approximation. Additionally, an efficiency comparison between the proposed estimator and some well-known existing estimators of the population mean has been conducted. Furthermore, certain empirical studies have corroborated the theoretical derivations, and the findings indicate that employing two auxiliary variables in estimating the population parameters in the presence of nonresponse is more profitable in terms of mean square error reduction.