The use of technologies and the Internet poses problems and risks related to digital security. This article presents the results of a study on the evaluation of the digital competence of future teachers in the DigCompEdu European framework. 317 undergraduate students from Spain and Portugal answered a questionnaire with 59 items, validated by experts, in order to assess the level and predominant competence profile in initial training (including knowledge, uses and interactions and attitudinal patterns). The results show that 47% of the participants belong to the profile of teachers at medium digital risk, evidencing habitual practices that involve risks such as sharing information and digital content inappropriately, not using strong passwords, and ignoring concepts such as identity, digital "footprint" and digital reputation. The average valuations of each item in the seven categories show that future teachers have an average competence in the area of digital security. They have good attitudes toward security but less knowledge and fewer skills and practices related to the safe and responsible use of the Internet. Future lines of work are proposed, aimed at responding to the demand for a better prepared and more digitally competent citizenry. The demand for education in security, privacy and digital identity is becoming increasingly important, and these elements form an essential part of initial training.