To limit climate warming to 2°C above preindustrial levels, most economic sectors will need a rapid transformation toward a net zero emission of CO2. Tuna fisheries is a key food production sector that burns fossil fuel to operate but also reduces the deadfall of large-bodied fish so the capacity of this natural carbon pump to deep sea. Yet, the carbon balance of tuna populations, so the net difference between CO2 emission due to industrial exploitation and CO2 sequestration by fish deadfall after natural mortality, is still unknown. Here, by considering the dynamics of two main contrasting tuna species (Katsuwonus pelamis and Thunnus obesus) across the Pacific since the 1980s, we show that most tuna populations became CO2 sources instead of remaining natural sinks. Without considering the supply chain, the main factors associated with this shift are exploitation rate, transshipment intensity, fuel consumption, and climate change. Our study urges for a better global ocean stewardship, by curbing subsidies and limiting transshipment in remote international waters, to quickly rebuild most pelagic fish stocks above their target management reference points and reactivate a neglected carbon pump toward the deep sea as an additional Nature Climate Solution in our portfolio. Even if this potential carbon sequestration by surface unit may appear low compared to that of coastal ecosystems or tropical forests, the ocean covers a vast area and the sinking biomass of dead vertebrates can sequester carbon for around 1000 years in the deep sea. We also highlight the multiple co-benefits and trade-offs from engaging the industrial fisheries sector with carbon neutrality.