Safe Emergency Response Act This bill directs the Department of Homeland Security (DHS) to suspend immigration enforcement operations and initiatives, including initiatives associated with evacuations or sheltering and the use of checkpoints within an area for which the President has declared a major disaster or an emergency. State and local immigration enforcement participation, including lawful detentions of non-citizens, shall be suspended except in cases specifically identified by DHS and communicated to the state or locality that pose an urgent and individualized threat to public safety or national security. With respect to persons in state or local detention during a major disaster or an emergency, DHS is urged to support state and local law enforcement agencies to prioritize the safety needs of their communities and individual detainees.