Nuclear propulsion is necessary for successful Mars exploration to enhance crew safety and reduce mission costs. Safety concerns are considered by some to be an implements to the use of nuclear thermal rockets for these missions. Therefore, an assessment was made of the various types of possible accident conditions that might occur and whether design or operational solutions exist. With the previous work on the NERVA nuclear rocket, most of the issues have been addressed in some detail. Thus, a large data base exist to use in an agreement. The assessment includes evaluating both ground, launch, space operations and disposal conditions. The conclusion is that design and operational solutions do exist for the safe use of nuclear thermal rockets and that both the environment and crews be protected against harmful radiation. Further, it is concluded that the use of nuclear thermal propulsion will reduce the radiation and mission risks to the Mars crews.