Extant work documents pronounced ideological disagreement over climate action, with rightist voters becoming increasingly skeptical of climate protection measures. This divide poses a major challenge to effective climate governance. However, little is known about why rightist voters reject climate action and how political parties could sway these voters’ preferences in support of more ambitious climate action. Based on a pre-registered factorial survey experiment among a conservative-leaning sample of 5500 voters in Germany, this paper provides a detailed assessment of conservative voters’ climate attitudes and tests the effects of a conservative pro-climate narrative. Leveraging insights from political psychology, the paper argues that presenting climate action in connection to conservative core values like tradition, obedience, and social order should increase support for climate action among rightist voters. The results demonstrate that although conservative voters are concerned about the green transition of the economy, they primarily worry about its economic aspects rather than its environmental necessity. The findings also demonstrate that presenting climate action in connection to conservative values can be a viable political strategy – especially, for centre-right parties. This highlights the potential of a conservative pro-climate narrative in building the broad societal consensus needed for the green transition of the economy.