Given concerns about the ambition and effectiveness of current climate pledges, a case has been made for the integration of demand-side policies such as carbon pricing with supply-side bans on fossil fuel extraction. However, little is known about their interplay in the context of climate stabilization strategies. Here, we present the first multi-model assessment quantifying the effectiveness of supply-side policies and their interactions with demand-side ones. We design narratives of fossil fuel bans and explore a variety of scenarios with four integrated assessment models, to find that widespread international supply side policies significantly reduce emissions but not at sufficient levels to stabilize temperature increase to well below 2°C. When combined with demand-side policies, supply side policies reduce the required carbon price to meet the Paris goals, dampen reliance on CO2 removal and increase investment in renewable energy. The results indicate the opportunity to introduce fossil fuel bans alongside price-based, demand-focused policies when exploring climate neutrality pathways.