Background In the case of people who carry an increased number of anxiety traits due to their maladaptive coping strategies, psychosocial stressors may further increase the level of perceived stress they experience. In our research study, we aimed to examine perceived stress and health anxiety levels as well as coping styles among students at one of the higher education institutions in Hungary, in the midst of the COVID-19 pandemic.Methods A cross-sectional study was conducted using an online-based survey at the University of Debrecen, during the official lockdown in Hungary when dormitories were closed, and teaching was conducted using online platforms. Our questionnaire solicited information using three international scales, namely, the Perceived Stress Scale (PSS), the Ways of Coping Questionnaire (WCQ), and the Short Health Anxiety Inventory (SHAI).Results A total of 1320 students have participated in our study, of whom 6 responses were excluded due to incompleteness. Among the remaining 1314 participants, 948 (72.1%) and 366 (27.9%) were Hungarian and international students, respectively. Female students predominated the overall sample with 939 participants (71.5%). In general, there was a statistically significant positive relationship between perceived stress and health anxiety. Health anxiety and perceived stress levels were significantly higher among international students compared to the Hungarian ones. Also, the elevation in perceived stress was significantly greater among students who mostly used emotion-focused coping strategies, both in the Hungarian and in the international student samples. Besides, a higher proportion of international students used emotion-focused coping methods compared to Hungarian students. Concerning health anxiety, female students (Hungarian and international) had significantly higher levels of health anxiety compared to males. Moreover, female students had significantly higher levels of perceived stress compared to males in the international group, however, there was no significant difference in perceived stress between males and females in the Hungarian group. Conclusion People’s elevated perceived stress levels during major life events can be further deepened by disengagement from home by using inadequate coping methods. By following and adhering to international recommendations that primarily convey problem-focused strategies, people’s emotional-focus strategies and the associated higher levels of perceived stress may be mitigated.