A method is developed for constructing the part of the axial-exchange-current operator that is associated with the nucleon-nucleon interaction from a general complete interaction model. By calculating the coefficients in the corresponding effective single-nucleon axial-current operator we find that the axial exchange current associated with the nucleon-nucleon interaction contributes only about 2% to the quenching of the axial-current coupling constant. The main causes of the large quenching found in shell-model analyses are, therefore, the model-dependent axial-exchange-current operators that cannot be determined from the interaction and second-order configuration mixing in the nucleon wave functions.