The COVID-19 outbreak and governmental measures to keep the population safe had a great impact on many aspects of society, including well-being. Using data from N = 1281 participants from six countries (Argentina, France, Greece, Italy, Japan, and Turkey), we first explored differences in anxiety, depression (measured with the Hospital Anxiety and Depression Scale; HADS), and time perspectives (Zimbardo Time Perspective Inventory; ZTPI), between these countries during the first weeks of the pandemic. We observed that Turkish participants reported the highest levels of anxiety, and Japanese and Greek the lowest. For depression symptoms, the Japanese scored highest and Italians lowest. Next, for each country, we investigated how well the relatively time-stable personality traits of time perspectives, chronotype (reduced Morningness-Eveningness Questionnaire; rMEQ), and Big Five personality traits (short Big Five Inventory; BFI) predicted the levels of anxiety and depression (HADS). The regression analyses showed that negative attitudes towards the past predicted the levels of both anxiety and depression in most of the countries we analyzed. Additionally, in many countries, a Past Positive orientation negatively predicted depression whereas the Present Fatalistic subscale predicted anxiety and depression. The chronotype did not contribute additionally to the models. The Big Five traits (and particularly neuroticism) showed substantial incremental explanatory power for anxiety in some countries but did not consistently predict anxiety levels. For depression, the additional variance accounted for by including the BFI as predictors was rather small. Importantly, the ZTPI subscales were retained as significant predictors in the model still when the BFI and rMEQ were considered as potential predictors. Our results yield evidence that the ZTPI time perspectives are valuable predictors for anxiety and depression levels during the first period of the pandemic.