Today, the Climate models (CM) are the main tools for forecasting sea level rise (SLR) at global and regional scales. The CM forecasts are accompanied by inherent uncertainties. Understanding and reducing these uncertainties is becoming a matter of increasing urgency in order to provide robust estimates of SLR impact on coastal societies, which need sustainable choices of climate adaptation strategy. These CM uncertainties are linked to structural model formulation, initial conditions, emission scenario and internal variability. The internal variability is due to complex non-linear interactions within the Earth Climate System and can induce diverse quasi-periodic oscillatory modes and long-term persistences. To quantify the effects of internal variability, most studies used multi-model ensembles or sea level projections from a single model ran with perturbed initial conditions. However, large ensembles are not generally available, or too small, and computationally expensive. In this study, we use a power-law scaling of sea level fluctuations, as observed in many other geophysical signals and natural systems, which can be used to characterize the internal climate variability. From this specific statistical framework, we (1) use the pre-industrial control run of the National Center for Atmospheric Research Community Climate System Model (NCAR-CCSM) to test the robustness of the power-law scaling hypothesis; (2) employ the power-law statistics as a tool for assessing the spread of regional sea level projections due to the internal climate variability for the 21st century NCAR-CCSM; (3) compare the uncertainties in predicted sea level changes obtained from a NCAR-CCSM multi-member ensemble simulations with estimates derived for power-law processes, and (4) explore the sensitivity of spatial patterns of the internal variability and its effects on regional sea level projections.