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BACKGROUND: Zinc (Zn) deficiency in crops is commonly aggravated by high levels of phosphorus (P) in soil. In this work, the initial performance of pot‐growing maize in response to the available P and Zn in soils with low available Zn and to the application of P and Zn fertilizers was investigated. RESULTS: The soils (six non‐calcareous and 14 calcareous) ranged widely in available P (Olsen P: 5.5–37.9 mg kg−1), were poor in available Zn [diethylenetriaminepentaacetic acid‐extractable Zn (ZnDTPA): 0.20–0.84 mg kg−1] and had an Olsen P/ZnDTPA ratio of 13 to 111 mg mg−1. Soil P application generally increased aerial dry matter (ADM) yield; Zn increased ADM yield mostly when applied in combination with P; and the sole application of Zn increased yield only in a soil with a high (28 mg kg−1) Olsen P and a low (0.36 mg kg−1) ZnDTPA. The increase in ADM yield resulting from optimal application of P and/or Zn to the soil was modest in soils where the Olsen P/ZnDTPA ratio was 30–60 and Olsen P was >14 mg kg−1. Zinc uptake by the control plants was correlated with the ZnDTPA of the soil. For a certain ZnDTPA value, the level of plant available Zn was higher in non‐calcareous than in calcareous soils. CONCLUSION: Soil application of fertilizer P and Zn, in soils with low levels of available Zn, should not only aim at increasing the available P and Zn levels but also balancing them at the appropriate Olsen P/ZnDTPA ratio, which was found to lie in the 30–60 range in the present study. © 2020 Society of Chemical Industry [ABSTRACT FROM AUTHOR]