Firefighters in Southern California on Wednesday began to contain a fire that erupted in Malibu late Monday night and has burned nearly 4,000 acres, destroyed several structures and forced thousands to evacuate the area.

Overnight, firefighters were able to contain 7 percent of the Franklin fire after battling strong winds on Tuesday, according to the California Department of Forestry and Fire Protection.

Chief Anthony C. Marrone of the Los Angeles County Fire Department said at a news conference on Tuesday night that officials were still assessing the full scope of the damage, but their preliminary review found that at least seven structures had been destroyed and eight had been damaged.

No injuries or deaths have been reported.

Nearly 20,000 residents were in the mandatory or voluntary evacuation zones, and officials urged them to continue to avoid the area until the fire was under control.

“The entire fire area remains under threat,” Chief Marrone said.

Inspection teams were expected to begin assessing the damage on Wednesday, Chief Marrone said.

Among those whose homes were damaged because of the fire was Bruce Silverstein, a Malibu City Council member, who said in an interview that fire appeared to have entered his home through the chimney and burned one side of the home on the inside.

Mr. Silverstein evacuated after the fire began and sought shelter at a hotel in nearby Santa Monica before returning home later on Tuesday to see the damage.

“The house is going to be uninhabitable,” he said on Tuesday night as he drove toward Los Angeles with his wife to visit their son before staying again at the hotel. “It needs a major, major amount of work.”

More than two million residents in Southern California, including the Malibu area, remained under a red flag warning through Wednesday night, meaning that weather conditions were still conducive to helping wildfires spread quickly.

Chief Marrone said that strong winds and low humidity would “continue to challenge firefighters on the line and in the air as they struggle to contain the stubborn fire.” Crews also have had to battle steep terrain in the Santa Monica Mountains above Malibu.

Some of the strongest winds appeared to have passed on Tuesday, according to weather reports, but the dry conditions could continue to fuel the Franklin fire before a chance of rain on Thursday.