The government programs aimed at the development of universities, especially those that support research activities exist in many countries. In 2021 the Russian “Project 5-100” has been replaced by the “PRIORITY 2030” program (Strategic Academic Leadership Program). It emphasizes the importance of analyzing the factors that influence various scientific indicators of the Russian universities. This study examines the indicators of the quantity (number of publications) and quality (number of citations) of research activity of Russian universities in three main databases (WoS, Scopus, RSCI) and the influence of different factors on them: educational, economic, structural, and those related to internationalization. The research is based on the data of performance monitoring of higher educational establishments that provides results of 49 largest Russian universities over the last four years. The main research method is econometric analysis using panel data models. The results of the study showed that the indicators of internationalization (the number of foreign employees and the number of foreign graduate students) and the number of grants have the greatest influence on the indicators of universities in international databases. The number of citations is also influenced by the number of defended PhD dissertations for the reporting year and there is some evidence that the share of extra-budgetary income of the university is also important. The number of publications is influenced by the quality of student enrollment, the ratio of staff salaries to the regional average, and the share of full-time employees. In the case of the university indicators in the RSCI database (mainly consisting of Russian publications), the factors differ from the abovementioned: in the model for the number of publications, the quality of enrollment of students and the number of foreign graduate students ceases to be significant, while the indicators of the share of extra-budgetary income and the share of employees with a scientific degree become significant. The share of full-time employees is also significant, where it shows direct correlation. This study can help university management work out strategies to improve various scientific indicators.