The metal abundance of the hot plasma that permeates galaxy clusters represents the accumulation of heavy elements produced by billions of supernovae. Therefore, X-ray spectroscopy of the intracluster medium provides an opportunity to investigate the nature of supernova explosions integrated over cosmic time. In particular, the abundance of the iron-peak elements (chromium, manganese, iron and nickel) is key to understanding how the progenitors of typical type Ia supernovae evolve and explode. Recent X-ray studies of the intracluster medium found that the abundance ratios of these elements differ substantially from those seen in the Sun, suggesting differences between the nature of type Ia supernovae in the clusters and in the Milky Way. However, because the K-shell transition lines of chromium and manganese are weak and those of iron and nickel are very close in photon energy, high-resolution spectroscopy is required for an accurate determination of the abundances of these elements. Here we report observations of the Perseus cluster, with statistically significant detections of the resonance emission from chromium, manganese and nickel. Our measurements, combined with the latest atomic models, reveal that these elements have near-solar abundance ratios with respect to iron, in contrast to previous claims. Comparison between our results and modern nucleosynthesis calculations disfavours the hypothesis that type Ia supernova progenitors are exclusively white dwarfs with masses well below the Chandrasekhar limit (about 1.4 times the mass of the Sun). The observed abundance pattern of the iron-peak elements can be explained by taking into account a combination of near- and sub-Chandrasekhar-mass type Ia supernova systems, adding to the mounting evidence that both progenitor types make a substantial contribution to cosmic chemical enrichment.