In the context of globalization, ICT is increasingly applied in a wide range of educational activities, especially during the outbreak of the COVID-19 pandemic. In Vietnam, switching from face-to-face to online teaching has been one of the fulfilled objectives of continuing educational activities. This paper is among the first studies to evaluate primary school students' transversal competencies in this context. Through an online survey, 661 fifth-grade students self-assessed their transversal competencies, e.g. problem-solving skills, creative skills, ICT skills, and social and cross-cultural skills. ANOVA analysis revealed that the use of ICT skills and social and cross-cultural skills among students in private schools is greater than that of students in public schools. In addition, the results of the Pearson correlation analysis pointed out that students' transversal competencies have a strong positive correlation with online learning activities. These findings not only contribute to supporting Vietnamese educational institutions and educational policymakers to adjust online teaching activities to enhance transversal competencies for primary school students but are also a valuable reference for countries with similar backgrounds.