Psychological distress is widespread globally, affects both mental and physical health, and has been significantly exacerbated by the COVID-19 pandemic. Reliable and valid instruments to assess psychological distress are needed so that interventions to address this condition can be directed and evaluated. We evaluated the psychometric statistics of the Depression Anxiety Stress Scales (DASS-21) using the Rasch method and a population survey sample dataset from four nations. To meet the requirements of the Rasch model, we randomly selected 500 participants (at least 110 from each country) from a total sample of 1822 individuals from Germany (n = 475), Ghana (n = 523), India (n = 411), and New Zealand (n = 413). Minor testlet modifications were necessary to achieve a satisfactory model fit for the depression (χ2 (30) = 40.32, p = 0.099), anxiety (χ2 (32) = 31.22, p = 0.510), and stress (χ2 (20) = 29.64, p = 0.076) subscales, and the full-scale (χ2 (18) = 23.93, p = 0.16). The scales were strictly unidimensional with acceptable reliability reflected by Person Separation Index (PSI) values of 0.86 for depression, 0.74 for anxiety, 0.82 for stress, and 0.87 for the total scale. The scales’ items showed invariance across the countries and sociodemographic factors. The scales also demonstrated convergent, structural, and external validities. The study supported the reliability and validity of the DASS-21 for assessing psychological distress in four countries. Rasch model algorithms developed in this study enable conversion of the ordinal DASS-21 scale and its subscale scores to interval-level scores, which increases the precision of measurement. Future studies should apply Rasch methodology to the DASS-21 in various cultural contexts, incorporating subgroup analyses.