We consider a full-duplex (FD) multiuser system where an FD base station (BS) is designed to simultaneously serve both downlink (DL) and uplink (UL) users in the presence of half-duplex eavesdroppers (Eves). The problem is to maximize the minimum (max-min) secrecy rate (SR) among all legitimate users, where the information signals at the FD-BS are accompanied with artificial noise to debilitate the Eves' channels. To enhance the max-min SR, a major part of the power budget should be allocated to serve the users with poor channel qualities, such as those far from the FD-BS, undermining the SR for other users, and thus compromising the SR per-user. In addition, the main obstacle in designing an FD system is due to the self-interference (SI) and co-channel interference (CCI) among users. We therefore propose an alternative solution, where the FD-BS uses a fraction of the time block to serve near DL users and far UL users, and the remaining fractional time to serve other users. The proposed scheme mitigates the harmful effects of SI, CCI, and multiuser interference, and provides system robustness. The SR optimization problem has a highly nonconcave and nonsmooth objective, subject to nonconvex constraints. For the case of perfect channel state information (CSI), we develop a low-complexity path-following algorithm, which involves only a simple convex program of moderate dimension at each iteration. We show that our path-following algorithm guarantees convergence at least to a local optimum. Then, we extend the path-following algorithm to the cases of partially known Eves' CSI, where only statistics of CSI for the Eves are known, and worst-case scenario in which Eves can employ a more advanced linear decoder. The merit of our proposed approach is further demonstrated by extensive numerical results.