MEXICO CITY (AP) — Mexico's newly elected president held out an olive branch Monday to the more than one-third of Mexicans who didn't vote for her, but the first woman to win the job faces a tough path toward reconciling a country left deeply divided by outgoing President Andrés Manuel López Obrador.

Claudia Sheinbaum promised to continue the political course set by her populist predecessor despite widespread discontent with persistent cartel violence and disappointing economic performance.

"Even though the majority of the people backed our project, our duty will always be to look out for each and every Mexican, without distinctions," the preident-elect said in her victory speech, after long-delayed initial vote counts gave her a crushing margin of victory, higher even than the one López Obrador won in 2018.

With about 78% of votes counted, Sheinbaum had some 59% of votes, about twice as many as her nearest competitor Xóchitl Gálvez, who got around 28%.

"Even though there are many Mexicans who don't fully agree with our project, we must walk in peace and harmony," Sheinbaum said.

But it will be four months until Sheinbaum can take office, and López Obrador appeared determined Monday to push through his highly divisive Constitutional changes — many of which opponents fear will fatally weaken Mexico's democracy — before he leaves office on Sept. 30.

López Obrador's Morena party, which he founded and in which he remains far more personally popular than Sheinbaum, appeared to be on track to win the two-thirds majority needed to change the Constitution. López Obrador has already laid out 20 constitutional changes he plans to submit, including the elimination of independent oversight and regulatory agencies.

That troubles some in Mexico.

"The climate of political polarization has gotten worse during the current administration," Moody's Analytics Director Alfredo Coutiño wrote in a report Monday. "The country is significantly divided and will require the new president's political leadership to restore national unity."

For the moment, López Obrador struck a note more celebratory than vengeful, though throughout most of his six-year term he has piled far more contempt on journalists and opponents than on the country's drug cartels, which he has not confronted.

"This is something really historic," López Obrador said of the election of the first woman to Mexico's presidency. "We are living through exceptional, extraordinary, glorious times."

López Obrador also repeated his pledge to allow Sheinbaum to govern, without trying to rule from behind the scenes after he leaves office.

"Let it be heard loud and clear, after I finish my term in office, I will retire and I will never again participate in any public or political act," he said.

Sheinbaum, a climate scientist and former Mexico City mayor, has vowed to continue López Obrador's policies, and in her victory speech Monday gave little sign of how she will make her own mark on the presidency. Her cool temper offers a sharp contrast in style with López Obrador's folksy populism, and a break with Mexico's male-dominated political culture.

Sheinbaum said Sunday night that her two competitors called her and conceded in an election that guaranteed Mexico would make history. The two leading candidates were women, and Sheinbaum is also the first person from a Jewish background to lead the overwhelmingly Catholic country.

Sara Ríos, 76, a retired literature professor at Mexico's National Autonomous University, expressed confidence Sheinbaum will reconcile the country.

"The only way that we move forward is by working together," Ríos said. "She is going to work to bring peace to the country, and is going to manage to advance, but it is a slow process."

The elections were widely seen as a referendum on López Obrador, who has expanded social programs but largely failed to reduce cartel violence in Mexico. The 61-year-old Sheinbaum is unlikely to enjoy the kind of unquestioning devotion that López Obrador has enjoyed.

In Mexico City's main plaza, the Zocalo, Sheinbaum's lead did not draw the kind of cheering, jubilant crowds that greeted López Obrador's victory in 2018. Those present were enthusiastic, but comparatively few in number.

Fernando Fernández, a chef, 28, joined the relatively small crowd, hoping for a Sheinbaum victory, but even he acknowledged there were problems.

"You vote for Claudia out of conviction, for AMLO," Fernández said, referring to López Obrador by his initials, as most Mexicans do.

But his highest hope is that Sheinbaum can "improve what AMLO couldn't do, the price of gasoline, crime and drug trafficking, which he didn't combat even though he had the power."

Sheinbaum stressed the long struggle it took for a woman to reach the presidency.

"I do not arrive alone," she said. "We all arrived, with our heroines who gave us our homeland, with our mothers, our daughters and our granddaughters."