To mitigate the negative effects of false information more effectively, the development of automated AI (artificial intelligence) tools assisting fact-checkers is needed. Despite the existing research, there is still a gap between the fact-checking practitioners' needs and pains and the current AI research. We aspire to bridge this gap by employing methods of information behavior research to identify implications for designing better human-centered AI-based supporting tools. In this study, we conducted semi-structured in-depth interviews with Central European fact-checkers. The information behavior and requirements on desired supporting tools were analyzed using iterative bottom-up content analysis, bringing the techniques from grounded theory. The most significant needs were validated with a survey extended to fact-checkers from across Europe, in which we collected 24 responses from 20 European countries, i.e., 62% active European IFCN (International Fact-Checking Network) signatories. Our contributions are theoretical as well as practical. First, by being able to map our findings about the needs of fact-checking organizations to the relevant tasks for AI research, we have shown that the methods of information behavior research are relevant for studying the processes in the organizations and that these methods can be used to bridge the gap between the users and AI researchers. Second, we have identified fact-checkers' needs and pains focusing on so far unexplored dimensions and emphasizing the needs of fact-checkers from Central and Eastern Europe as well as from low-resource language groups which have implications for development of new resources (datasets) as well as for the focus of AI research in this domain.