Objective Word recognition, fluency, vocabulary, and working memory have been established as predictors of reading comprehension in the first elementary school grades. However, the additional role of reasoning is not so clear. The aim of this study was to investigate the effect of word recognition, fluency, vocabulary, working memory, verbal, and non‐verbal reasoning on reading comprehension, focusing on the additional effect of reasoning when the effects of the other variables are controlled. Method A group of 159 students from the second and fourth grades was assessed. Results The results indicated that all variables are correlated with reading comprehension and that the effect size varies according to the school grade. Hierarchical multiple linear regression analyses revealed that in second grade, fluency was the strongest predictor of reading comprehension and that reasoning had no effect on reading comprehension, after controlling for the previous variables. However, in the fourth grade, non‐verbal reasoning was the only significant unique predictor of reading comprehension, after accounting for the influence of the other variables. Conclusions These results highlight the importance of promoting the mastery of accurate and fluent reading in the lower grades while promoting reasoning abilities in the higher grades.