Allowing Monte Carlo (MC) codes to perform fuel cycle calculations requires coupling to a point depletion solver. In order to perform depletion calculations, one-group cross sections must be provided in advance. This paper focuses on generating accurate one-group cross-section values using Monte Carlo transport codes. The proposed method is an alternative to the conventional direct reaction rate tally approach, which requires substantial computational effort. The method presented here is based on the multigroup approach, in which pregenerated multigroup sets are collapsed with MC calculated flux. In our previous studies, we showed that generating accurate one-group cross sections requires their tabulation against the background cross section (σ0) to account for the self-shielding effect in the unresolved resonance energy range.However, in previous studies, the model used for the calculation of σ0 was simplified by relying on user-specified Bell and Dancoff factors. This work demonstrates that the one-group cross-section values calculated under the previous simplified model assumptions may not always agree with the directly tallied values. More specifically, the assumption is not universally applicable to the analysis of reactor systems with different neutron spectra and may be inaccurate when the number of energy groups is reduced (i.e., from tens of thousands to hundreds of groups). Therefore, the original background cross-section model was extended by implicitly accounting for the Dancoff and Bell factors. The method developed here reconstructs the correct value of σ0 by utilizing statistical data generated within the MC transport calculation by default. The proposed method was implemented in the BGCore code system. The one-group cross-section values generated by BGCore were compared with those tallied directly from the MCNP code. Very good agreement in the one-group cross-section values was observed. The method does not carry any additional computational burden, and it is universally applicable to the analysis of thermal as well as fast reactor systems. Adopting this multigroup methodology, which accounts for self-shielding, allows generation of highly accurate cross sections even if the number of energy groups is significantly reduced (to hundreds versus tens of thousands of groups). This reduction considerably improves the computational efficiency, which makes the analysis of large-scale reactor problems feasible.