The owners of the Mid-Wilshire facility are selling it to UCLA Health.
The deal prevents the hospital from providing care beyond March 31. But council members want the hospital to delay the closure by at least six months.
The hospital mostly serves Black, Latino and low-income people who have been disproportionately affected by the pandemic.
"If this hospital were to close it would exacerbate the racial disparities we are seeing play out in this county during the COVID-19 pandemic," said Cathy Kennedy, vice president of the California Nurses Association.
The council motion says the staff at the hospital have reported severe shortfalls in patient care in anticipation of the closure.
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