The motion by Friends of King/Drew, part of a civil rights lawsuit alleging disproportionate impact on South Los Angeles, argued that the court needed to intervene immediately so that members of the community would not be deprived of emergency medical services.
The county, which operates the hospital south of Watts, argued that it has a plan for the patients.
Health department officials have said that they need to close King/Drew's trauma center to save the rest of the troubled hospital. They plan to close the unit Feb. 1.
California Hospital Medical Center south of downtown Los Angeles opened a trauma center this week that is expected to handle many of the trauma patients who would now go to King/Drew.
Some South Los Angeles officials and community groups fought the county's effort to close the King/Drew trauma center.