The first tropical storm to hit Los Angeles in more than 80 years unleashed furious floods across parts of Southern California more accustomed to drought, as officials urged the public to stay safe as they began to count the cost of damage.

The National Weather Service downgraded the hurricane to a tropical depression but not before California Governor Gavin Newsom declared a state of emergency for much of Southern California, with flash flood warnings until at least 3 a.m. (1000 GMT) on Monday.

Mountain and desert areas could get 5 to 10 inches (12 to 25 cm) of rare rain, as much as the deserts typically see in a year, forecasters said.

Los Angeles Mayor Karen Bass said she was still worried that people could let down their guard if Hilary left them initially unharmed but later bands of the storm swung back to surprise those who were not prepared.

"We know that it could get much worse," Bass told a news briefing on Sunday. "My concern is that people will be a little dismissive and go out when we need people to stay at home, to stay safe."

Hilary's center was expected to move quickly across Nevada on Monday, with the storm forecast to dissipate later in the day, the weather service said.

The storm had passed northward through Mexico's Baja California peninsula. It killed at least one person in Mexico, triggering flash flooding and sweeping away roads.

Images on social media showed raging, muddy torrents gushing down eroded streets.

It crossed the border on Sunday afternoon, hitting San Diego county with its first tropical storm ever recorded and becoming the first to pelt Los Angeles county since 1939.

San Bernardino county, to the east of Los Angeles, ordered evacuations of towns in the mountains and valleys where social media images showed torrents of water, mud, rock and trees.

In more populated Ventura county northwest of Los Angeles, the National Weather Service warned of life-threatening flooding from heavy rains, which dumped up to 2 inches (5 cm) of rain within two hours.

U.S. President Joe Biden ordered federal agencies to move personnel and supplies into the region.

Officials said Los Angeles county's 75,000 homeless people were especially vulnerable, as were hillside canyons and areas recently denuded by wildfires.

As a precaution, the two largest school districts in the state, in Los Angeles and San Diego, canceled school on Monday.

The storm stunned people in the nearby town of Rancho Mirage, where water and debris rushed over closed roads and stranded at least one pickup truck in water that rose nearly to the top of its bed.

"It's quite amazing. I've never seen anything like this," said Sean Julian, 54, a resident of the town. "I'm seeing a lot more trees down. And there's a big tree that just fell over there, and I probably shouldn't be out here." (Reporting by Reuters staff; Writing by Daniel Trotta; Editing by Clarence Fernandez)