Children’s language skills, which are related to later academic and employment outcomes, differ by socioeconomic background as early as the age of 3 years. Previous studies have shown the detrimental effects of both excessive media consumption and low levels of parent-child book reading on early language development. However, the question of whether the social gap in language development is mediated by these activities has received little attention in previous research. The aim of this study was to examine the relationship between socioeconomic status, as indicated by maternal educational attainment and material hardship during pregnancy, and children’s communication skills at 3 years of age, taking into account the mediating role of daily screen time and parent-child book reading frequency at 18 months of age. Relevant data from the Cohort ’18 Growing Up in Hungary birth cohort study were available for 2,006 children (51% male, 49% female). Data on parenting activities and child development were provided by the mothers. Children’s communication skills were measured using the Ages and Stages Questionnaire-3 screening tool. Children's daily screen time and frequency of parent-child book reading at age 18 months varied significantly by socioeconomic status in bivariate analyses, as did communication skills at 3 years of age. The proportion of children with delayed communication skills at 3 years of age was higher for children of mothers with low (14.3%) and medium (13.6%) compared to high (6.7%) educational attainment. The results from the mediation analyses indicated that screen time and parent-child book reading frequency at 18 months mediated the relationship between maternal educational attainment and delayed communication skills at 3 years. Meanwhile, material hardship mediated the relationship between maternal educational attainment and the aforementioned activities. In conclusion, social differences in digital media use and parent-child book reading frequency contribute to the social gap in language skills.