Excessive screen use in early school age is associated with worsened health habits and negative child development in later age. We aimed to assess the time spent on modern and traditional screen-based devices and examine its associations with socio-demographic characteristics. This population-based cross-sectional observation study was conducted in Czechia, Slovakia and Finland between April and June 2021. Participants (N = 1,915) were parents/caregivers of children attending elementary school grades 1 to 3, selected by stratified random sampling. Children's daily leisure screen time (LST) based on parental reports was the main outcome. Descriptive statistics, mean comparison and linear regression analysis were used for the analysis. The average daily LST was found to be as high as 3.5 hours and significantly associated with most socio-demographic variables. Eighty percent of children exceeded the threshold of two hours of LST per day, which was formerly introduced by the American Academy of Pediatrics. The most important predictor of LST in children was having their screen-based device(s) for their exclusive personal use (EPU). Linear regression with all predictors assessed together confirmed the significant effect of the screen-based devices' EPU, the child's sex and grade, the child's birth order and the parent's education, even when controlled for media parenting practices. Given the widespread availability of smartphones for exclusive personal use among young children, the regulation of EPU and the reinforcement of effective media parenting practices, particularly in families with lower education and income, are critical public health strategies to mitigate the negative impact of excessive screen time on child development and overall well-being.