Los Angeles Fire Department personnel rescued a man and his dog from the Los Angeles River Monday.

Around 2:45 p.m. PT, authorities received a report from a bystander that a man had jumped into the water to rescue his dog. Fire crews responded and found that the dog had managed to swim to the edge and escape the rapids.

The dog was taken to a shelter for temporary care.

At a press conference Monday night, officials said LA County Fire had rescued 16 people from flooding conditions and five cats.

A flash flood warning that covers the Los Angeles-area cities of Glendale, Pasadena and Santa Clarita has been extended until 6 p.m. local time.

A flood advisory covering all of LA County is in effect until 3 p.m. local time.

Three people have been killed by fallen trees during the monster storm slamming California.

A man in Carmichael died after a tree fell on him, a Sacramento County spokesperson said Monday.

A tree fell on a house in Boulder Creek on Sunday, killing one resident inside, according to the Santa Cruz Sheriff’s Department. A second person managed to escape the home, authorities said.

The third fatality was recorded in Yuba City. An 82-year-old man was in his backyard on Sunday when he was killed by a falling redwood tree, Yuba City police said.

Flash flooding and mudslides are an ongoing threat from Santa Barbara to San Diego on Monday, with the Los Angeles area in the bull’s-eye, as a historic atmospheric river storm slams Southern California.

Ten inches of rain fell in some areas of Southern California. Many spots saw more than a month’s worth of rain over the last 24 hours.

Los Angeles recorded over 4 inches of rain in 24 hours, marking the city’s wettest day since December 2004.

The heavy rain and flooding will continue through Tuesday morning. Another 2 to 4 inches of rain is possible from Los Angeles to San Diego.

By Tuesday afternoon, the downpours will wind down. By Wednesday morning, the showers will linger in Southern California and most of the heavy rain will move into Arizona.

-ABC News’ Melissa Griffin

"This storm continues -- and that means we still need Angelenos to take precautions," Los Angeles Mayor Karen Bass warned Tuesday.

Periods of rain will continue Tuesday creating dangerous conditions on the roads and increasing the chance of mudslides and flooding, Los Angeles Fire Department Chief Kristin Crowley said.

No fatalities have been reported in LA, Bass said.

Crews have responded to 307 mudslides and 257 fallen trees, Crowley said.

If you must go outside, use caution, Crowley warned. Slow down if driving and always be on the lookout for downed power lines and trees, she said.

The mayor commended residents who have checked on each other in hard-hit communities and stressed that everyone should check on their neighbors.

The "historic" rain is expected to taper off late Tuesday night, National Weather Service meteorologist Ariel Cohen said.

There’s a chance for more atmospheric rivers this spring, Cohen said.