Abstract Background Children's numerical and arithmetic skills differ greatly already at an early age. Although research focusing on accounting for these large individual differences clearly demonstrates that mathematical performance draws upon several cognitive abilities, our knowledge concerning key abilities underlying mathematical skill development is still limited. Aims First, to identify key cognitive abilities contributing to children's development of early arithmetic skills. Second, to examine the extent to which early arithmetic performance and early arithmetic development rely on different or similar constellations of domain‐specific number abilities and domain‐general cognitive abilities. Sample In all, 134 Swedish children ( M age = 6 years and 4 months, SD = 3 months, 74 boys) participated in this study. Method Verbal and non‐verbal logical reasoning, non‐symbolic number comparison, counting knowledge, spatial processing, verbal working memory and arithmetic were assessed. Twelve months later, arithmetic skills were reassessed. A latent change score model was computed to determine whether any of the abilities accounted for variations in arithmetic development. Results Arithmetic performance was supported by counting knowledge, verbal and non‐verbal logical reasoning and spatial processing. Arithmetic skill development was only supported by spatial processing. Conclusions Results show that young children's early arithmetic performance and arithmetic development are supported by different cognitive processes. The findings regarding performance supported Fuchs et al.'s model ( Dev Psychol , 46 , 2010b, 1731) but the developmental findings did not. The developmental findings align partially to Geary et al.'s ( J Educ Psychol , 109 , 2017, 680) hypothesis stating that young children's early arithmetic development is more dependent on general cognitive abilities than number abilities.