Context: Requirements issues tend to be mitigated in organizations with high process maturity levels since they do their business in a systematic, consistent and proactive approach. In a Safety-Critical System (SCS), requirements problems have been associated with accidents and safety incidents. Objective: This work investigates which safety practices/actions are suitable to be used in the Requirements Engineering (RE) process of SCS and how to design a safety maturity model for this area. Method: we adopted different empirical techniques to propose Uni-REPM SCS, which consists of a safety module to be included in the Unified Requirements Engineering Process Maturity Model (Uni-REPM). Results: The safety module has seven main processes, 14 sub-processes and 148 safety actions describing principles and practices that form the basis of safety processes maturity. Conclusions: Preliminary validation with two practitioners and nine academic experts indicates that the safety module can help organizations to evaluate their current safety practices with respect to their RE process. Moreover, it also offers a step-wise improvement strategy to raise their safety maturity level. © 2018 IEEE.