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Forests are the main source of biomass production from solar energy and take up around 2.4 +/- 0.4 PgC per year globally. Future changes in climate may affect forest growth and productivity. Currently, state-of-the-art Earth system models use prescribed wood harvest rates in future climate projections. These rates are defined by integrated assessment models (IAMs), only accounting for regional wood demand and largely ignoring the supply side from forests. Therefore, we assess how global growth and harvest potentials of forests change when they are allowed to respond to changes in environmental conditions. For this, we simulate wood harvest rates oriented towards the actual rate of forest growth. Applying this growth-based harvest rule (GB) in JSBACH, the land component of the Max Planck Institute's Earth system model, forced by several future climate scenarios, we realized a growth potential 2 to 4 times (3-9 PgC yr(-1)) the harvest rates prescribed by IAMs (1-3 PgC yr(-1)). Limiting GB to managed forest areas (MF), we simulated a harvest potential of 3-7 PgC yr(-1), 2 to 3 times higher than IAMs. This highlights the need to account for the dependence of forest growth on climate. To account for the long-term effects of wood harvest as integrated in IAMs, we added a life cycle analysis, showing that the higher supply with MF as an adaptive forest harvesting rule may improve the net mitigation effects of forest harvest during the 21st century by sequestering carbon in anthropogenic wood products.