Abstract Background Problem‐solving in early and middle childhood is of high relevance for cognitive developmental research and educational support. Previous research on science problem‐solving has focussed on the process and strategies of children handling challenging tasks, but less on providing insights into the cognitive network that enables science problem‐solving. Aims In this study, we aimed to investigate whether performance in science problem‐solving is mainly determined by domain‐specific rule knowledge, by domain‐general cognitive abilities or both. Methods In our study, 215 6‐ to 8‐year‐old children completed a set of three domain‐specific rule knowledge tasks and three corresponding problem‐solving tasks that were content‐coherent, as well as a vocabulary task, and a reasoning task. Results Correlational and regression analyses revealed a negligible impact of domain‐specific rule knowledge on corresponding problem‐solving tasks. In contrast, the associations between problem‐solving performance in different domains and the associations between problem‐solving performance and domain‐general abilities (vocabulary and reasoning) were comparably strong. Conclusions The findings suggest that science problem‐solving in primary school children primarily relies on domain‐general cognitive abilities. Implications of these findings are discussed with regard to cognitive theories and early science education.