Villaraigosa told the Los Angeles Times that he respects the protesters right to peacefully assemble and express their views, but they must respect city laws and regulations.
San Francisco police have already cleared two encampments. Most recently, police estimated at least five protesters were arrested and several others injured in a clash Tuesday evening.
Some cities, such as Providence, R.I., are moving ahead with plans to evict activists. But from Tampa, Fla., to Boston, police and city leaders say they will continue to try to work with protesters to address problems in the camps.
In Oakland, officials initially supported the protests, with Mayor Jean Quan saying that sometimes "democracy is messy."
But tensions reached a boiling point after a sexual assault, a severe beating and a fire were reported and paramedics were denied access to the camp, according to city officials. They also cited concerns about rats, fire hazards and public urination.
Demonstrators disputed the city's claims, saying that volunteers collect garbage and recycling every six hours, that water is boiled before being used to wash dishes and that rats have long infested the park.
When riot gear-clad police moved in early Tuesday, they were pelted with rocks, bottles and utensils from people in the camp's kitchen area. They emptied the camp near city hall of people, and barricaded the plaza.
Protesters were taken away in plastic handcuffs, most of them arrested on suspicion of illegal lodging.
Demonstrators returned later in the day to march and retake the plaza. They were met by police officers in riot gear. Several small skirmishes broke out and officers cleared the area by firing tear gas.
The scene repeated itself several times just a few blocks away in front of the plaza.
Tensions would build as protesters edged ever closer to the police line and reach a breaking point with a demonstrator hurling a bottle or rock, prompting police to respond with another round of gas.
The chemical haze hung in the air for hours, new blasts clouding the air before the previous fog could dissipate.
The number of protesters diminished with each round of tear gas. Police estimated that there were roughly 1,000 demonstrators at the first clash following the march. About 100 were arrested.
On Wednesday, Oakland officials allowed protesters back into the plaza but said people would be prohibiting from spending the night, potentially bringing another clash with police.
About 1,000 people quickly filled the area, but later many of them filed out and began their march. By early Thursday, about 50 people were left at the site and few police could be seen.
In Atlanta, police in riot gear and SWAT teams arrested 53 people in Woodruff Park, many of whom had camped out there for weeks as part of a widespread movement that is protesting the wealth disparity between the rich and everyone else.
Mayor Kasim Reed had been supportive of the protests, twice issuing an executive order allowing them to remain.
Reed said on Wednesday that he had no choice to arrest them because he believed things were headed in a direction that was no longer peaceful. He cited a man seen walking the park with an AK-47 assault rifle.
"There were some who wanted to continue along the peaceful lines, and some who thought that their path should be more radical," Reed said. "As mayor, I couldn't wait for them to finish that debate."
Reed said authorities could not determine whether the rifle was loaded, and were unable to get additional information.
An Associated Press reporter talked to the man with the gun earlier Tuesday.
- Live at the GOP convention: Donald Trump...
- Marilyn Monroe's tresses and dresses going up...
- IOC explores legal options on banning all...
- Utah pledges all votes to Cruz after Trump...
- Trump's party: What to watch on GOP...
- Friends recall slain officers as residents...
- No sign of Trump endorsement, but plenty of...
- Trump speechwriter apologizes for Melania...
- Utah delegates finally stand and cheer... 93
- Utah GOP delegates finally fired up... 74
- Obama rejects Trump depiction of US in... 39
- The day after: Lee defends Cruz at GOP... 31
- Trump speechwriter apologizes for... 27
- Police give all-clear in Munich... 25
- Thunderous boos for Cruz for refusing... 22
- Ohio Mormon offered invocation at... 22