The increasing awareness of privacy and the adoption of data regulations challenge the traditional trajectory publication framework in which a trusted server has access to the raw data from mobile clients. In the new untrusted environment, the clients call for much stronger data privacy preservation locally without sharing their raw data. Based on the emerging paradigm of federated analytics, we propose a Federated Analytics-based Secure Trajectory PUBlication (FASTPub) mechanism to operate in such untrusted environments. Compared with existing local differential privacy (LDP) methods, FASTPub guarantees LDP and loss-bounded $k$-anonymity simultaneously with greatly improved data utility. Specifically, FASTPub works interactively between the server and clients and iteratively builds up the trajectory without exposing raw data. Sampled clients only respond to selected trajectory fragments with randomized answers to preserve privacy as much as possible. The server then intelligently aggregates these randomized responses leveraging the intrinsic Apriori property and a Markov independent assumption of trajectory data to guide further iterations. Extensive experiments on synthetic and real-world datasets on two downstream tasks demonstrate that FASTPub gains a remarkably improved data utility compared to the existing state-of-the-art solutions.