Knowledge of the occurrence and mobility of carbonate-rich melts in the Earth's mantle is important for understanding the deep carbon cycle and related geochemical and geophysical processes. However, our understanding of the mobility of carbonate-rich melts remains poor. Here we report viscosities of carbonate melts up to 6.2 GPa using a newly developed technique of ultrafast synchrotron X-ray imaging. These carbonate melts display ultralow viscosities, much lower than previously thought, in the range of 0.006-0.010 Pa s, which are similar to 2 to 3 orders of magnitude lower than those of basaltic melts in the upper mantle. As a result, the mobility of carbonate melts (defined as the ratio of melt-solid density contrast to melt viscosity) is similar to 2 to 3 orders of magnitude higher than that of basaltic melts. Such high mobility has significant influence on several magmatic processes, such as fast melt migration and effective melt extraction beneath mid-ocean ridges.