( CNN ) -- A wildfire scorching Southern California prompted authorities to urge thousands to evacuate on Tuesday , though authorities appear to have gotten a better grip on the blaze as the day wore on . `` At the point that the fire is right now , we have a pretty good handle on it , '' San Diego Fire Chief Javier Mainar told reporters early Tuesday evening . `` We hope to do some more work through the night and into tomorrow , but I think that the largest part of the emergency has passed . '' At one point late Tuesday afternoon , San Diego County announced on Twitter and its emergency department website that `` more than 20,000 homes and residences are being evacuated due to the Bernardo Fire . '' But in a news conference Tuesday evening , County Sheriff Bill Gore that only 5,000 evacuation notices had been issued ; he said that the 20,000 number may have come from an assumption of four people in each residence . Authorities initially said that most of the evacuations were in San Diego city limits . But by the evening , San Diego Police Chief Shelley Zimmerman estimated about 300 homes were still evacuated in select areas . Earlier , parents were told to pick up their children from three elementary schools because of the fire and an evacuation center was moved from one high school to another . Mainar , though , said he did n't see any reason now why classes in those elementary schools would not resume Wednesday . The fire began at 10:45 a.m. ( 1:45 p.m . ET ) , fanned by strong winds , according to the fire chief . `` It has been , to say the least , a very challenging day for local fire agencies and law enforcement agencies , '' Mainar said . `` It is unusual in May to have wind driven fires like this that prove to be such a challenge to contain . '' For all those challenges , authorities said they do n't know of any injuries or fatalities tied to the blaze . It had burned 800 acres and was 5 % contained as of 7:50 p.m. , according to CalFire . The National Weather Service issued a red flag warning for areas around San Diego through 8 p.m. Wednesday . As the agency noted , `` a red flag warning means that critical fire weather conditions are either occurring now or will shortly , '' with strong winds , low humidity and warm temperatures feeding into `` extreme fire behavior . '' Temperatures in the Southern California city are forecast to peak in the mid-90s Wednesday and Thursday with no sign of rain , before cooling somewhat later in the week . CNN 's Matthew Stucker contributed to this report .
NEW : Fire chief : `` The largest part of the emergency has passed '' NEW : City police chief says 300 are still evacuated . NEW : 800 acres have burned , and the fire is 5 % contained . A red flag warning is in effect for areas around San Diego .