The transient climate response to cumulative carbon emissions (TCRE) is a key metric in estimating the remaining carbon budget for given temperature targets. However, the TCRE has a small scenario dependence that can be non-negligible for stringent temperature targets. To investigate the parametric correlations and scenario dependence of the TCRE, the present study uses a 512-member ensemble of an Earth system model of intermediate complexity (EMIC) perturbing 11 physical and biogeochemical parameters under scenarios with steady increases of 0.25%, 0.5%, 1%, 2%, or 4% per annum (ppa) in the atmospheric CO ₂ concentration (pCO ₂ ), or an initial increase of 1% followed by an annual decrease of 1% thereafter. Although a small difference of 5% (on average) in the TCRE is observed between the 1-ppa and 0.5-ppa scenarios, a significant scenario dependence is found for the other scenarios, with a tendency toward large values in gradual or decline-after-a-peak scenarios and small values in rapidly increasing scenarios. For all scenarios, correlation analysis indicates a remarkably large correlation between the equilibrium climate sensitivity (ECS) and the relative change in the TCRE, which is attributed to the longer response time of the high ECS model. However, the correlations of the ECS with the TCRE and its scenario dependence for scenarios with large pCO ₂ increase rates are slightly smaller, and those of biogeochemical parameters such as plant respiration and the overall pCO ₂ –carbon cycle feedback are larger, than in scenarios with gradual increases. The ratio of the TCREs under the overshooting (i.e., 1-ppa decrease after a 1-ppa increase) and 1-ppa increase only scenarios had a clear positive relation with zero-emission commitments. Considering the scenario dependence of the TCRE, the remaining carbon budget for the 1.5 °C target could be reduced by 17 or 22% (before and after considering the unrepresented Earth system feedback) for the most extreme case (i.e., the 67 ^th percentile when using the 0.25-ppa scenario as compared to the 1-ppa increase scenario). A single ensemble EMIC is also used to indicate that, at least for high ECS (high percentile) cases, the scenario dependence of the TCRE should be considered when estimating the remaining carbon budget.