Currently, the International Maritime Organization (IMO) has approved and implemented the assessment requirement for Minimum Propulsion Power (MPP) of ships in adverse sea conditions. The assessment method and relevant influence factors will have a vital impact on ship's design and operation. On the other hand, MPP is essentially a criterion for manoeuvring safety at actual seas. However, the practical assessment methods adopted in IMO guidelines do not directly and accurately account for ship's course-keeping ability in severe seas. A time-domain comprehensive method with supplementary course-keeping ability criteria has been proposed in the authors' preliminary research. Based on an updated mathematical model and criteria, this paper presents more detailed elaborations, results and discussions on the time-domain method, including the comparative analyses with a power line method and two steady-state equilibrium methods based on IMO guidelines and draft. Discussions on the influences of key factors, involving criterion conditions and calculation parameters, are also presented. The results indicate that different methods exhibit varying advantages and complexity in MPP assessment, thus constituting a multi-level assessment framework for MPP. In particular, the time-domain comprehensive assessment has a higher accuracy with more realistic description of manoeuvre behaviors, capable of offering a solution for the ships that cannot meet other assessments, or for the assessment requiring additional course-keeping ability. Furthermore, an expanded range of wave direction sets a stricter but potentially necessary requirement, while using the self-propulsion factors at low speeds can eliminate the unnecessary conservation of assessment result caused by those at design speed.