Fruit and vegetable (FV) intake is declining in New Zealand, and over half of New Zealand’s children do not meet the recommendation of two serves of fruit and three serves of vegetables daily (with even lower adherence among children in high-deprivation neighbourhoods). The aim of this study was to map the potential causal pathways explaining this decline and possible actions to reverse it. Semi-structured interviews were held in April–May 2018 with 22 national actors from the produce industry, food distribution and retail sector, government, and NGO health organisations. The qualitative systems dynamics method of cognitive mapping was used to explore causal relationships within the food system that result in low FV intake among children. Barriers and solutions identified by participants were analysed using thematic analysis and according to a public health intervention framework. Participants were in agreement with the goal of improving FV intake for health and economic outcomes, and that health promotion strategies had been ineffectual to date due to multiple systemic barriers. Common barriers discussed were poverty, high food prices, low skills/knowledge, unhealthy food environments, climate change, and urbanization. Solutions with the strongest evidence of efficacy identified by the participants were subsidizing FVs and early childhood interventions to improve FV exposure.