Police were making more arrests after at least 10 on Sunday and 29 the previous night, Los Angeles police officers told a news briefing.
National Guard troops guarded federal government buildings, as police and protesters clashed in separate demonstrations over federal immigration raids in Los Angeles.
Los Angeles police declared several rallies to be "unlawful assemblies", accusing some protesters of throwing concrete projectiles, bottles and other items at police.
Video images showed several self-driving cars from Alphabet s Waymo were set ablaze on a downtown street on Sunday evening.
Los Angeles police officers on horseback attempted to control the crowds.
Demonstrators shouted "Shame on you!" at police and some appeared to throw objects, video images showed. One group blocked the 101 Freeway, a major downtown thoroughfare.
Groups of protesters, many carrying Mexican flags and signs denouncing U.S. immigration authorities, gathered in spots around the city.
Read more: Trump deploys National Guard as Los Angeles protests against immigration agents continue
The Los Angeles branch of the Party for Socialism and Liberation organized speakers outside City Hall for an afternoon rally.
California Governor Gavin Newsom said he requested the Trump administration to withdraw its order to deploy 2,000 National Guard troops in Los Angeles county, calling it unlawful.
In an interview with MSNBC, Newsom said he planned to sue the administration over the deployment, adding that Trump "has created the conditions" around the protests.
Newsom accused Trump of trying to manufacture a crisis and violating California s state sovereignty. "These are the acts of a dictator, not a president," he wrote in a post on X.
However, Police Chief Jim McDonnell told a media briefing on Sunday night that the protests were getting out of control.
Asked if the National Guard was needed, McDonnell said police would not "go to that right away," but added, "Looking at the violence tonight, I think we ve got to make a reassessment."
In a social media post, Trump called on McDonnell to do so.
"He should, right now!!!" Trump added. "Don’t let these thugs get away with this. Make America great again!!!"
The White House disputed Newsom s characterization, saying in a statement, "Everyone saw the chaos, violence and lawlessness."
