Although large scale nuclear power deployment can reduce greenhouse gas emissions, potential for nuclear power to reduce climate mitigation cost is not well understood. We use an energy system model to estimate the relative savings in mitigation costs enabled by nuclear power as well as their robustness via scenario and Monte Carlo analysis. Nuclear power reduces mitigation costs in all explored scenarios, but the extent varies considerably. Nuclear power reduces costs significantly if carbon storage capacity is low but is replaceable if the capacity is abundant and technology available. The same holds for the cost of renewables. However, providing a full cost benefit analysis of nuclear power is beyond the scope of this paper.