The use of different bias‐correction methods and global retrospective meteorological forcing data sets as the reference climatology in the bias correction of general circulation model (GCM) daily data is a known source of uncertainty in projected climate extremes and their impacts. Despite their importance, limited attention has been given to these uncertainty sources. We compare 27 projected temperature and precipitation indices over 22 regions of the world (including the global land area) in the near (2021–2060) and distant future (2061–2100), calculated using four Representative Concentration Pathways (RCPs), five GCMs, two bias‐correction methods, and three reference forcing data sets. To widen the variety of forcing data sets, we developed a new forcing data set, S14FD, and incorporated it into this study. The results show that S14FD is more accurate than other forcing data sets in representing the observed temperature and precipitation extremes in recent decades (1961–2000 and 1979–2008). The use of different bias‐correction methods and forcing data sets contributes more to the total uncertainty in the projected precipitation index values in both the near and distant future than the use of different GCMs and RCPs. However, GCM appears to be the most dominant uncertainty source for projected temperature index values in the near future, and RCP is the most dominant source in the distant future. Our findings encourage climate risk assessments, especially those related to precipitation extremes, to employ multiple bias‐correction methods and forcing data sets in addition to using different GCMs and RCPs.