This paper elucidates the importance of intercultural competence in teaching English as a Foreign Language (EFL) to a multicultural group of students in a matriculation preparation programme in Israel. It is based on an action research employing a case study approach to explore the role of cultural background in the acquisition of EFL. Drawing from intercultural competence theories, it is claimed that while cultural background plays a notable role in students’ entry level and approach to learning EFL, in general, and reading competence, in particular, it does not play a determining role in their progress and achievements. Rather, students with high intercultural skills, regardless of cultural background, entered a dialogue and engaged with students of other cultures, which was associated with an ability to enter a dialogue and engage with a text in English. Students’ intercultural competence was evolved by the creation of a ‘classroom culture’ where structured and unstructured activities guided by the teacher spurred engagement and negotiation processes between students of various cultural backgrounds to increase intercultural competence and English reading comprehension abilities.