Meaning-oriented oral language skills, including morphological awareness and vocabulary, have been identified as key predictors of reading comprehension. In addition, empirical evidence highlights the important role of cognitive functions like planning and attention in reading comprehension processes. However, the combined influence of these linguistic and cognitive factors on reading comprehension difficulties remains underexplored. This cross-sectional study investigated the unique contributions of vocabulary, morphological awareness, planning, and attention to different aspects of reading comprehension in third- and fourth-grade students who experience difficulties in reading comprehension but demonstrate adequate reading fluency. The sample included 33 children with reading comprehension difficulties and 41 typically developing children, selected from a pool of 143 Greek-speaking students with typical non-verbal ability. Group classification was based on a cut-off approach using performance on reading comprehension measures, excluding children with reading fluency difficulties. Participants completed two standardized reading comprehension tasks, each engaging distinct cognitive processes, along with a word reading fluency task. They were subsequently assessed on oral receptive vocabulary, morphological awareness, planning, and attention. Children with reading comprehension difficulties scored lower than typically developing children in vocabulary, morphological awareness, and attention. Hierarchical regression analyses revealed that vocabulary was the only significant predictor of reading comprehension in both groups, after controlling for age and reading fluency. Among children with reading comprehension difficulties, morphological awareness significantly contributed to their performance on the more cognitively demanding reading comprehension task, even after controlling for vocabulary. Despite certain limitations, these findings underscore the prominent role of meaning-oriented oral language skills—rather than cognitive skills—in reading comprehension difficulties during the middle grades of primary education in an alphabetic language with a shallow orthographic system and rich morphological structure.