Knowledge of the rheology of molten materials at high pressure and temperature is required to understand magma mobility and ascent rate at conditions of the Earth's interior. We determined the viscosity of nominally anhydrous sodium carbonate (Na2CO3), an analogue and ubiquitous component of natural carbonatitic magmas, by the in situ “falling sphere” technique at 1.7, 2.4 and 4.6 GPa, at 1200 to 1700 °C, using the Paris-Edinburgh press. We find that the viscosity of liquid Na2CO3 is between 0.0028 ± 0.0001 Pa·s and 0.0073 ± 0.0001 Pa·s in the investigated pressure-temperature range. Combination of our results with those from recent experimental studies indicate a negligible dependence on pressure from 1 atm to 4.6 GPa, and a small compositional dependence between molten alkali metal-bearing and alkaline earth metal-bearing carbonates. Based on our results, the viscosity of Na2CO3 is consistent with available viscosity data of both molten calcite (determined at high pressure and temperature) and Na2CO3 at ambient pressure. Molten Na2CO3 is a valid experimental analogue for study of the rheology of natural and/or synthetic near-solidus carbonatitic melts. Estimated values of the mobility and ascent velocity of carbonatitic melts at upper conditions are between 70 and 300 g cm−3·Pa−1·s−1 and 330–1450 m·year−1, respectively, when using recently proposed densities for carbonatitic melts. The relatively slow migration rate allows magma-rock interaction over time causing seismic anomalies and chemical redox exchange.