Claudia Sheinbaum, a climate scientist and former mayor of Mexico City, won her nation’s elections on Sunday in a landslide victory that brought a double milestone: She became the first woman, and the first Jewish person, to be elected president of Mexico.

Early results indicated that Ms. Sheinbaum, 61, prevailed in what the authorities called the largest election in Mexico’s history, with the highest number of voters taking part and the most seats up for grabs.

It was a landmark vote that saw not one, but two, women vying to lead one of the hemisphere’s biggest nations. And it will put a Jewish leader at the helm of one of the world’s largest predominantly Catholic countries.

Ms. Sheinbaum, a leftist, campaigned on a vow to continue the legacy of Mexico’s current president and her mentor, Andrés Manuel López Obrador, which delighted their party’s base — and raised alarm among detractors. The election was seen by many as a referendum on his leadership, and her victory was a clear vote of confidence in Mr. López Obrador and the party he started.

Mr. López Obrador has completely reshaped Mexican politics. During his tenure, millions of Mexicans were lifted out of poverty and the minimum wage doubled. But he has also been a deeply polarizing president, criticized for failing to control rampant cartel violence, for hobbling the nation’s health system and for persistently undercutting democratic institutions.

Still, Mr. López Obrador remains widely popular and his enduring appeal propelled his chosen successor. And for all the challenges facing the country, the opposition was unable to persuade Mexicans that their candidate was a better option.

“We love her, we want her to work like Obrador,” Gloria Maria Rodríguez, 78, from Tabasco, said of Ms. Sheinbaum. “We want a president like Obrador.”

Ms. Sheinbaum won with at least 58.3 percent of the vote, according to preliminary results, while her closest competitor, Xóchitl Gálvez, an entrepreneur and former senator on a ticket with a coalition of opposition parties, had at least 26.6 percent.

If early returns hold, Ms. Sheinbaum will have captured a broader share of the vote than any candidate in decades.

Speaking to supporters early Monday, Ms. Sheinbaum vowed to work on behalf of all Mexicans, reaffirmed her party’s commitment to democracy and celebrated her groundbreaking ascension to the nation’s highest office.

“For the first time in 200 years of the republic, I will become the first female president of Mexico,” she said. “And as I have said on other occasions, I do not arrive alone. We all arrived, with our heroines who gave us our homeland, with our ancestors, our mothers, our daughters and our granddaughters.”

Ms. Sheinbaum said she received calls from Ms. Gálvez and the third-place candidate, Jorge Álvarez Máynez, to congratulate her on the victory. Shortly after Ms. Sheinbaum’s speech, Ms. Gálvez told supporters that the early returns were “not favorable to my candidacy,” and “irreversible,” noting that she had just communicated with Ms. Sheinbaum.

Ms. Gálvez had said in an interview days before the vote on Sunday that “an anti-system vote” against Mr. López Obrador could help propel her to victory. In reality, it appeared that many Mexicans still associate the parties backing her with a system they see as inept and corrupt.

“Xóchitl Gálvez has been unable to represent change because the parties backing her embody the establishment,” said Carlos Bravo Regidor, a political analyst based in Mexico City. “Most Mexicans want a continuity of the change brought by López Obrador.”

Many voters seemed to endorse Ms. Sheinbaum as an agent of institutionalizing the changes brought about by her mentor. “We need to bring about more change to the country,” said Evelyn Román, 21, a chemical engineering student in Mexico City who supports Ms. Sheinbaum. “We did notice the progress in these six years.”

Ms. Sheinbaum’s experience is ample: She has a Ph.D in energy engineering, participated in a United Nations panel of climate scientists awarded a Nobel Peace Prize and governed the capital, one of the largest cities in the hemisphere.

Known as a demanding boss with a reserved demeanor, Ms. Sheinbaum has risen through the ranks by aligning herself completely with Mr. López Obrador, who built an entire political party around his outsize personality. During the campaign, she backed many of his most contentious policies, including a slate of constitutional changes that critics say would severely undermine democratic checks and balances.

As a result, the president-elect battled the perception among many Mexicans that she will be little more than a pawn of her mentor.

“There’s this idea, because a lot of columnists say it, that I don’t have a personality,” Ms. Sheinbaum complained to reporters earlier this year. “That President Andrés Manuel López Obrador tells me what to do, that when I get to the presidency, he’s going to be calling me on the phone every day.”

Even with the broad mandate voters granted her, she faces significant challenges when she takes office in October.

Mr. López Obrador benefited “from the invincible popularity that comes from being a very charismatic leader — something that Claudia is not,” said Paula Sofía Vásquez, a political analyst based in Mexico City.

Cartel violence continues to torment the country, displacing people en masse and fueling one of the deadliest campaign cycles in recent Mexican history, with more than 36 people vying for public office killed since last summer.

Carlos Ortiz, 57, a municipal official working for the Iztapalapa borough in Mexico City, said that such bloodshed compelled him to vote against Ms. Sheinbaum.

“I want everything to change,” Mr. Ortiz said, recalling the dozens of aspirants for public office killed in recent months. “I don’t want a country on fire anymore.”

Mr. López Obrador has directed government attention to addressing the drivers of crime instead of waging war on the criminal groups, a strategy he called “hugs not bullets.” Homicides declined modestly but remain near record levels, and reports of missing people have spiked. Insecurity was a top concern for voters.

Ms. Sheinbaum has said she would continue his focus on social causes of the violence, while also working to lower rates of impunity and building up the national guard.

On the economy, the opportunities are clear: Mexico is now the largest trading partner of the United States, benefiting from a recent shift in manufacturing away from China. The currency is so strong it’s been labeled the “super peso.”

But there are also problems simmering. The federal deficit ballooned to around 6 percent this year, and Pemex, the national oil company, is operating under a mountain of debt, straining public finances.

“The fiscal risk we’re facing at the moment is something we haven’t seen for decades,” said Mariana Campos, director of Mexico Evaluates, a public policy research group.

It’s unclear how Ms. Sheinbaum would make good on a range of campaign promises — from building public schools and new health clinics to expanding social welfare programs — given the current state of public finances.

“The problem I see is that a lot of proposals are oriented toward spending and there is nowhere to get the money from,” said Ms. Vásquez, the political analyst.

Another challenge involves the broad new responsibilities granted to the armed forces, which have been tasked with running ports and airports, running an airline, and building a railroad through the Mayan jungle. Ms. Sheinbaum has said “there is no militarization” of the country, while suggesting she’s open to re-evaluating the military’s involvement in public enterprises.

Beyond the domestic strains, Ms. Sheinbaum’s destiny will be intertwined with the outcome of the presidential election in the United States.

A re-election victory for President Biden would provide continuity, but a return of Donald J. Trump to the White House would likely be far less predictable. Mr. Trump’s plans to round up undocumented people on a vast scale and deport them to their home countries could target millions of Mexicans living in the United States. He has already threatened to slap 100 percent tariffs on Chinese cars made in Mexico.

Then there’s the festering issue of fentanyl, which cartels produce in Mexico using chemicals imported from China, the U.S. government says. Mr. Trump has suggested taking military action to combat the fentanyl trade.

Ms. Sheinbaum has said Mexico would have “good relations” with either Mr. Trump or Mr. Biden as president, and her campaign team has said it will continue to work to contain flows of migrants.

But handling such pressure from Washington, even in the form of incendiary campaign rhetoric, could prove complicated.

Voters expressed faith in Ms. Sheinbaum’s ability to deal with such challenges. Daniela Mendoza, 40, a psychologist who lives in Villahermosa, in Tabasco state, said she had long supported Mr. López Obrador, including during his previously unsuccessful bids to win the presidency.

Pleased with his social welfare programs, Ms. Mendoza voted for Ms. Sheinbaum.

“Claudia follows that line, perhaps with better ideas,” Ms. Mendoza said. “And having the first woman president in the country is an accomplishment.”