President Biden on Tuesday called for the departure of the three council members in the nation’s second-largest city. “He believes they should all resign,” Karine Jean-Pierre, the White House press secretary, said. “The language that was used and tolerated in that conversation was unacceptable, and it was appalling.”

The recorded conversation involving some of Los Angeles’s top power brokers exposed the racial and ethnic factions that have come to dominate politics in California. But it also highlighted the political impatience among leaders of the city’s largest ethnic group: Latinos, who make up roughly half of the city’s population but who hold only four of its 15 City Council seats.

Los Angeles is a kind of microcosm of the world; its roughly four million residents speak a combined 200-plus languages at home. Over the decades, the assorted constituencies have tried to develop a coalition style of politics based on common interests in the heavily Democratic city, but, beneath that veneer, the reality often has been a quest for power and political spoils.

The recording was a conversation among Nury Martinez, the Council president; Gil Cedillo and Kevin de León, council members; and Ron Herrera, the leader of the powerful Los Angeles County Federation of Labor, that took place in October 2021 during intense negotiations over City Council redistricting.

Ms. Martinez is heard comparing the Black child of Councilman Mike Bonin to a “changuito,” Spanish for little monkey, and joking with Mr. de León that Mr. Bonin carries the child around like a designer handbag. Those were only two of the offensive comments in the 80-minute recording, which included ugly remarks describing recent migrants from the Mexican state of Oaxaca and disparaging remarks about the trustworthiness of white liberals and a councilwoman who is of South Asian descent.

News of the recording was first reported on Sunday by The Los Angeles Times; by Monday night, Mr. Herrera had resigned from the labor federation and Ms. Martinez had relinquished her leadership post on the City Council, although she resisted calls for her to leave the Council entirely. Mr. Cedillo and Mr. de León also have resisted calls for them to step down from their council seats.

Although the raw language on the audio riveted the city, political observers said the recording was less a reflection of Los Angeles residents — who in polls largely express pride in the city’s diversity — than of the political climate in City Hall. Challenged by Covid-19, besieged with a succession of public corruption investigations and presented with the political opportunity of new political maps, Los Angeles local government has, in the past couple of years, been a hotbed of internecine conflict.

“As much as it was a racist, racial, ethnic disparagement of everyone in town, it was more about power,” Zev Yaroslavsky, a longtime Los Angeles leader who served for 40 years on the City Council and the county’s Board of Supervisors, said of the meeting.

“It was a raw power grab,” he said.

Mr. Cedillo and Mr. de León appeared on the dais near the start of Tuesday’s meeting and were greeted with shouted profanities from the packed gallery. They left after a brief discussion with Councilman Mitch O’Farrell, who was presiding over the meeting as president pro tem.

Outside, before the session, protesters chanted “fuera,” or “out” in Spanish, demanding that the three council members resign. Inside, the cacophonous demonstration was so relentless and deafening that the council members recessed, hoping, in vain, for calm.

Later, during the meeting, Mr. Bonin said through tears: “I take a lot of hits, and I know I practically invite a bunch of them. But my son? Man, that makes my soul bleed.”

Mr. O’Farrell, the council member leading the meeting, condemned the comments and the political maneuvering of his colleagues. “There are no excuses,” he said. “The court of public opinion has rendered a verdict, and the verdict is they all must resign.”

For more than a half-century, Los Angeles politics have been a study in demographic constituencies and race relations. Not for nothing is Rodney King’s plea during the 1992 riots often viewed as the city’s signature utterance: “Can we all get along?”

White Angelenos, particularly in the San Fernando Valley and on the city’s affluent Westside, have long controlled the city’s wealth and power, but they now represent only 28 percent of the population.

The city’s Black community, with a vibrant middle class and powerful community leaders like Tom Bradley, a former mayor, and Magic Johnson, the Los Angeles Lakers star, has long wielded clout. Still, Black Angelenos are leaving the city as many are priced out of the communities they have built over decades. Although 20 percent of the Council seats are held by Black elected officials, Black Angelenos make up only 8.8 percent of the population.

The city’s Asian community has become a rising political force with nearly 12 percent of the population. But Latinos make up the city’s largest ethnic group by far.

In recent years, young progressives who studied the Los Angeles riots in school have risen to power, learning from past racial and ethnic conflicts in the city. Labor organizations also have gained influence as their ranks have swelled with Latino workers following California’s battle over immigrant rights in the 1990s.

“There are naturally tensions,” said Mr. Yaroslavsky, who now teaches at the Luskin School of Public Affairs at the University of California, Los Angeles, which conducts annual surveys of Los Angeles County. “The question is how you deal with that tension. I think there’s been a lot of effort made in this city and county to manage it.”

Constance L. Rice, a veteran civil rights lawyer in the city, said that efforts to work together tended to intensify during zero-sum contests such as the redrawing of political boundaries that occurs each decade. A citizen advisory committee conducts Los Angeles’s redistricting process and recommends maps, but — unlike California’s statewide line-drawing by an independent commission — the final boundaries are determined by the City Council.

In years past, Ms. Rice said, lawyers with expertise in federal voting rights law wielded considerable influence on the drawing of local political boundaries. As the Supreme Court has eroded the federal Voting Rights Act, however, outside experts have wielded less clout and political battles have intensified, she said.

“It used to be all about maximizing rights and balancing power,” Ms. Rice said. “Now it’s ‘Game of Thrones.’”

As Angelenos processed the furor, calls for solutions focused on whether the city’s redistricting process had been changed — and whether it might have been corrupted. Council members said on Tuesday that they intended to seek an independent redistricting process that doesn’t allow them to draw their own political lines.

Stephen Jn-Marie, a pastor and longtime activist in Los Angeles, said he participated in a Zoom call with roughly 60 Black organizers to discuss the audio recordings on Sunday night. On Tuesday morning, he arranged a news conference ahead of the City Council meeting “so folks could get the word out about how we feel and what must be done to move forward.”

According to Mr. Jn-Marie, the questions arising about redistricting were the most important. “We are going to need to look at those maps,” he said. “Because of the fact that it was redistricting in the context of Black and Indigenous folks and minimizing their power, we are calling for an investigation.”

Adam Nagourney, Ken Bensinger and Corina Knoll contributed reporting.