This data article describes the dataset of the International COVID-19 Impact on Parental Engagement Study (ICIPES). ICIPES is a collaborative effort of more than 20 institutions to investigate the ways in which, parents and caregivers built capacity engaged with children's learning during the period of social distancing arising from global COVID-19 pandemic. A series of data were collected using an online survey conducted in 23 countries and had a total sample of 4,658 parents/caregivers. The description of the data contained in this article is divided into two main parts. The first part is a descriptive analysis of all the items included in the survey and was performed using tables and figures. The second part refers to the construction of scales. Three scales were constructed and included in the dataset: 'parental acceptance and confidence in the use of technology', 'parental engagement in children's learning' and 'socioeconomic status'. The scales were created using Confirmatory Factor Analysis (CFA) and Multi-Group Confirmatory Analysis (MG-CFA) and were adopted to evaluate their cross-cultural comparability (i.e., measurement invariance) across countries and within sub-groups. This dataset will be relevant for researchers in different fields, particularly for those interested in international comparative education.