A ferocious atmospheric river storm that has battered California for days began to taper off Tuesday, but officials warned that even small amounts of additional precipitation could set off landslides in rain-drenched Southern California.

Between Sunday and Monday, the storm dumped record-breaking amounts of rain on the Los Angeles basin and prompted millions of residents to stay home to avoid potential hazards. By Monday evening, Los Angeles officials had counted more than 120 mudslides and 25 damaged structures in the city, many situated in the hills above Hollywood and Beverly Hills.

Across Southern California, dozens of people had to be plucked from floodwaters and the raging sea, including one man in Los Angeles County who leaped into the raging Los Angeles River to try to save his dog. In the Baldwin Hills neighborhood, an avalanche of mud smashed through a bedroom of a home.

But overall, the region has not suffered the worst-case flooding and other effects for which it had prepared, said Lindsey Horvath, a Los Angeles County supervisor.

“Instead, the damage has been more like 1,000 cuts — sinkholes, downed trees, areas of erosion,” she said at a news conference on Monday night.

Firefighters evacuated 16 people in the Studio City neighborhood on Monday after two homes on Lockridge Road sustained significant damage from debris that the storm had sent rushing through the area.