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The atmospheric CO2 concentration increased by about 20 ppm from 6000 BCE to the pre-industrial period (1850 CE). Several hypotheses have been proposed to explain mechanisms of this CO2 growth based on either ocean or land carbon sources. Here, we apply the Earth system model MPI-ESM-LR for two transient simulations of climate and carbon cycle dynamics during this period. In the first simulation, atmospheric CO2 is prescribed following ice-core CO2 data. In response to the growing atmospheric CO2 concentration, land carbon storage increases until 2000 BCE, stagnates afterwards, and decreases from 1 CE, while the ocean continuously takes CO2 out of the atmosphere after 4000 BCE. This leads to a missing source of 166 Pg of carbon in the ocean–land–atmosphere system by the end of the simulation. In the second experiment, we applied a CO2 nudging technique using surface alkalinity forcing to follow the reconstructed CO2 concentration while keeping the carbon cycle interactive. In that case the ocean is a source of CO2 from 6000 to 2000 BCE due to a decrease in the surface ocean alkalinity. In the prescribed CO2 simulation, surface alkalinity declines as well. However, it is not sufficient to turn the ocean into a CO2 source. The carbonate ion concentration in the deep Atlantic decreases in both the prescribed and the interactive CO2 simulations, while the magnitude of the decrease in the prescribed CO2 experiment is underestimated in comparison with available proxies. As the land serves as a carbon sink until 2000 BCE due to natural carbon cycle processes in both experiments, the missing source of carbon for land and atmosphere can only be attributed to the ocean. Within our model framework, an additional mechanism, such as surface alkalinity decrease, for example due to unaccounted for carbonate accumulation processes on shelves, is required for consistency with ice-core CO2 data. Consequently, our simulations support the hypothesis that the ocean was a source of CO2 until the late Holocene when anthropogenic CO2 sources started to affect atmospheric CO2 .