LOS ANGELES — Rick Caruso, a billionaire real estate developer, and Representative Karen Bass are heading to a November runoff election to become mayor of Los Angeles, in a race that has focused on voters’ worries about public safety and homelessness in the nation’s second-largest city.

Though neither candidate earned more than 50 percent of the vote, which would have allowed them to win outright on Tuesday, they both comfortably outperformed their opponents. The runoff was declared by The Associated Press.

The liberal city’s surge of support for Mr. Caruso, a longtime Republican who changed his registration to Democratic days before declaring his candidacy, is likely to deepen the Democratic Party’s divisions on issues of crime, policing and racial justice. San Francisco voters also moved on Tuesday to recall Chesa Boudin, the city’s progressive district attorney.

Ms. Bass was widely seen as the front-runner in the crowded primary before Mr. Caruso’s entrance in February, but his lavish spending and tough-on-crime message quickly propelled him, leading several other candidates to drop out of the race to replace Mayor Eric Garcetti, who is term limited.

The developer of several popular luxury shopping centers, Mr. Caruso, 63, tightly tied his campaign to the spotless image he has cultivated in the faux town squares of those properties. His campaign spent nearly $41 million, including $39 million of his own money, much of it on television, digital and radio ads that seemed to blanket the airwaves in recent weeks, portraying him as a successful businessman who could “clean up” Los Angeles.

Mr. Caruso may face a steeper uphill climb during the general election if high-profile Democrats rally behind Ms. Bass.

A victory for Mr. Caruso would be a significant shift in this overwhelmingly liberal city, where Senator Bernie Sanders easily won the Democratic presidential primary two years ago. The city’s longstanding battles over housing, homelessness and crime have reached a new level of urgency during the pandemic.

Mr. Caruso has portrayed the city as one in deep decay, promising to hire 1,500 more police officers and build 30,000 shelter beds in 300 days. The message has resonated among voters who are deeply frustrated with homeless encampments throughout the city, visible on residential sidewalks, nestled in parks and sprawling under freeway overpasses.

Casting himself as an outsider, Mr. Caruso has blamed career politicians, including Ms. Bass, for the city’s ills. After voting in the predominantly Latino neighborhood of Boyle Heights, Mr. Caruso criticized his rival for suggesting that it could take more than four years to solve homelessness in the city.

But experts and critics say many of Mr. Caruso’s promises may not be possible because of federal court mandates that allow people to camp in public spaces, as well as the city’s byzantine zoning rules. Compared with leaders of other large cities, the mayor of Los Angeles has relatively little power. Much of the sprawling region is controlled by the six members of the Los Angeles County Board of Supervisors, who oversee a $38.5 billion budget.

Ms. Bass, 68, who spent years organizing in South Los Angeles after the 1992 riots before being elected to the State Legislature and then Congress, has described her campaign as a kind of homecoming and pledged to address questions of equity in this profoundly stratified city.

The campaign between the two is also poised to become a test of whether voters this year favor an experienced politician who has spent nearly two decades in government or an outsider running on his business credentials.

Latino voters are expected to play a pivotal role in the November election and will be courted aggressively by both candidates. Polling has also indicated a striking gender gap, with Black and Latino men more likely to choose Mr. Caruso over Ms. Bass.

Mr. Caruso’s critics, including an independent expenditure committee supporting Ms. Bass, frequently compare him to former President Donald J. Trump, an analogy he has rejected. Instead, Mr. Caruso and his supporters liken him to Michael R. Bloomberg, another party-switching billionaire who won three terms as mayor of New York.

Mr. Caruso had been a longtime Republican and donated generously to the party, but switched his registration to independent in 2019 and then became a Democrat this year, just before announcing his bid for mayor.

Mr. Caruso and his supporters contend that most voters in Los Angeles are not worried about his past support of Republican causes and candidates, including donations to candidates who have fought against abortion rights. Mr. Caruso has dismissed criticism from organizations like Planned Parenthood and insists he supports “a woman’s right to choose.”

Mr. Caruso’s campaign has been aided by several high-profile veteran Democratic advisers, including Ace Smith, Sean Clegg and Juan Rodriguez. The three advised Vice President Kamala Harris during her failed presidential campaign as well as Gov. Gavin Newsom, who easily fended off a recall election last year. Mr. Caruso’s team also included several advisers who helped Eric Adams’s successful bid for New York mayor last year.

Ms. Bass, the former chair of the Congressional Black Caucus, was on President Biden’s shortlist as a possible vice president. Her advisers expect her to be able to consolidate support among both local and national Democrats, which they believe will persuade voters in the overwhelmingly left-leaning city.

For the last four months, Mr. Caruso’s ads have been almost inescapable in Los Angeles, and he spent more than 10 times as much as Ms. Bass’s campaign did on television, digital and radio advertisements.

Rosario Guzmán, 82, who was voting on Tuesday at the Avalon Carver Community Center in South Los Angeles, said that she had not felt this unsafe in Los Angeles since she moved from Mexico more than four decades ago — and that she had placed her hopes in Mr. Caruso, whose ads she had seen frequently on television.

“I have faith in him, a lot of faith,” she said, citing his Roman Catholic beliefs as a reason for her conviction. (Speaking in Spanish, Ms. Guzmán repeatedly referred to Mr. Caruso as “Señor Corazón,” or Mr. Heart.)