Ensuring the temporal stability of national food production is crucial for avoiding sharp drops in domestic food availability. The average stability of individual crop yields and asynchrony among crop yield fluctuations are two candidate mechanisms to stabilize national food production. However, the quantification of their respective influence on the stability of national food production is lacking, as is the identification of the factors regulating both mechanisms. Using yield data for 138 crops and 115 countries over a 50-year period, we first show that the stability of total national yield mostly relies on the fluctuations of the yield of crops covering the largest share of cropland. The average yield stability of these crops exert a stabilizing effect on national food production that is twice as important as the one of the asynchronous yield fluctuations among them. Climate variability reduces the stability of national food production by synchronizing yield fluctuations among crops and destabilizing the yield of individual crops. However, our results suggest that increasing crop diversity can counteract the synchronizing effects of climate variability by enhancing asynchronous dynamics among crops. Irrigation can promote the average stability of individual crop yields but cannot compensate for the destabilizing effect of climate variability. Considering both the response of each crop to climatic variations and the dynamics emerging from crop baskets will help agricultural policies to ensure stable food supply at the national level.