Mechanisms of atmospheric CO₂ growth by 20 ppm from 6000 BCE to the pre-industrial period are still uncertain. We apply the Earth system model MPI-ESM-LR for two transient simulations of the climate–carbon cycle. An additional process, e.g. carbonate accumulation on shelves, is required for consistency with ice-core CO₂ data. 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.