At a Board of Supervisors meeting on Tuesday, county Public Health Director Dr. Barbara Ferrer said the order will "with all certainty" be extended unless there is a "dramatic change to the virus and tools at hand."
Ferrer's comments came during a debate over how long the county's moratorium on evictions should remain in place.
Last month, officials extended the county's "safer at home" order until at least May 15. The region's reopening would be based on a four-point plan whose prerequisites would have to be achieved before the easing of restrictions could begin.
The county has already started to begin easing some coronavirus restrictions, even though the region continues to see a rise in cases and deaths. On Monday, health officials reported an additional 38 deaths and 566 new cases in L.A. County.
Last week, select businesses were allowed to reopen to curbside pickup and L.A. County beaches are set to reopen on Wednesday for active recreational use.