We consider the uniqueness of ground states for combined power-type nonlinear scalar field equations involving the Sobolev critical exponent at high frequencies. The uniqueness of ground states at high frequencies in five and higher dimensions has been proved in Akahori et al. (Calc. Var. Partial Differential Equations 58:32, 2019). Moreover, that in three dimensions can be obtained from the result of Coles and Gustafson (Publ. Res. Inst. Math. Sci. 56:647–699, 2020). On the other hand, the uniqueness in four dimensions has not been completely revealed. The aim in this paper is to prove the uniqueness in three and four dimensions in a unified way. Thus, we obtain a complete answer to the uniqueness problem for ground states at high frequencies. From the point of view of limiting profile of ground states at infinite frequency which is known to be the Aubin–Talenti function, the uniqueness problem in three and four dimensions is more difficult than that in higher dimensions. In this paper, we employ the fixed-point argument developed in Coles and Gustafson (Publ. Res. Inst. Math. Sci. 56:647–699, 2020). Since the application of the argument of Coles and Gustafson (Publ. Res. Inst. Math. Sci. 56:647–699, 2020) to four dimensions is by no means straightforward, we need to construct some estimates for the perturbed resolvents which fit the fixed-point argument (see Proposition 1.2 and ( 1.17 )).