The impact of the COVID-19 pandemic has highlighted the need to strengthen health communication in times of crisis. This study aims to analyze the media agenda of press conferences on COVID-19 in Mexico during the first two phases of the pandemic, based on journalists’ questions. The study is based on framing theory. The method used was content analysis from a quantitative perspective. This method was explicitly applied to the final section of the conferences, which dealt with “questions from the press.” The results show that at the beginning of the pandemic, the press was more interested in the government’s management of the health crisis than in issues such as the prevention of the disease itself or the economic impact of the crisis on the country. Moreover, the main characteristic of the questions was that they were generally socially relevant. In conclusion, we found that in the media agenda of the Mexican conference, the frame of attribution of responsibility was prominent but in combination with the frames of conflict, human interest, morality, and economic consequences.