The numbers were startling: In March, Mexico’s government said, the country’s emergency call centers were flooded with more than 26,000 reports of violence against women, the highest since the hotline was created.

But Mexico’s president brushed aside his own cabinet’s announcement, suggesting, without evidence, that the vast majority of the calls for help were little more than pranks.

“Ninety percent of those calls that you’re referring to are fake,” said the president, Andrés Manuel López Obrador, when asked about the surge in calls at a recent news conference. “The same thing happens with the calls the metro gets about sabotage or bombs.”

Mr. López Obrador, a leftist populist, won the presidency more than a year ago by promising to transform Mexico into a more equal society, and he appointed the first cabinet with gender parity in Mexico’s history, giving prominent feminists top posts.

But the president has been unable to stem the daily murder of women in the country — and has, at times, appeared to dismiss the problem altogether.

Credit…Jose Luis Gonzalez/Reuters

When asked recently about femicide, the killing of women because of their gender, Mr. López Obrador said the issue “has been manipulated a lot in the media.” He blamed the killings on “the neoliberal model” and said “suddenly conservatives are dressing up as feminists” to attack him.

In March, when tens of thousands marched in the capital in the largest feminist protests in recent history, he said the movement was, partly, the work of political opponents “who want to see this government fail.”

Now, as the pandemic forces Mexicans to stay at home more often, Mr. López Obrador has been adamant that the crisis has not made life more dangerous for victims of domestic violence, because unlike in other countries, Mexicans “are accustomed to living together.”

While the United Nations has urged countries to step up measures against domestic violence during national lockdowns, Mr. López Obrador has called the Mexican family “exceptional” and “the most fraternal nucleus,” suggesting the bonds of kinship are shielding Mexican women from abuse.

“They said there was going to be domestic violence, and there wasn’t,” he said at a recent news conference, contradicting his own government’s statistics.

Credit…Jordi Ruiz Cirera for The New York Times

“He is the first president to outright deny that the violence is happening,” said Wendy Figueroa, the head of the National Network of Shelters, a group that oversees domestic violence shelters across the country.

Credit…Luis Antonio Rojas for The New York Times

This week, his administration was widely ridiculed after previewing a publicity campaign that urged would-be abusers to “not lose patience” and “breathe and count to 10”— messages that critics said had no chance of persuading men not to attack their wives or children.

One of the government videos depicted angry family members calming down after a narrator suggests waving “the white flag of peace” before “violence overcomes you.”

Martha Tagle, an opposition legislator, said the campaign “placed the responsibility for violence against women on the women themselves.”

The group responsible for organizing a feminist protest earlier this year wrote on Twitter that the Mexican government should “count to ten yourselves,” since “that’s the number of daily femicides in the country.” Candelaria Ochoa, the head of the National Commission to Prevent and Eradicate Violence Against Women, a federal agency, said the government was still fine-tuning the campaign to specifically condemn violence against women.

When asked about the president’s comments, Ms. Ochoa noted that most calls to the government’s 911 help line for all types of assistance are, in fact, pranks or non-urgent calls.

However, the government’s tally of the rise in domestic violence calls in March excluded calls that were not real emergencies, indicating that there had been a real increase.

Ms. Ochoa said that fewer women had been showing up at government-run offices that serve abused women, but she added that it was possible some women were less likely to venture out during the pandemic.

“Maybe women are not leaving their houses to report crimes or receive attention,” she said.

The president has also angered feminists by cutting the budget for day care centers. Last year, he abandoned a move that would have cut funding for domestic violence shelters after a swift backlash from human rights groups.

“He has suspended or eliminated programs that directly support the most vulnerable communities of women,” said Ms. Figueroa. The need for these services is particularly high now, she said.

The number of women and children seeking assistance at the network’s shelters has increased by 77 percent since social distancing measures took effect. In April, one of the most lethal months in recent years, about 11 women were murdered per day.

Despite the anger over his statements about domestic violence, Mr. López Obrador has been praised for elevating prominent advocates for women to the highest levels of government and giving them control over the government’s response to the violence.

Olga Sánchez Cordero, the interior minister, stood next to the president in a recent news conference and said “we have a patriarchal system,” where “violence against women must be acknowledged.” Among the president’s closest allies is Claudia Scheinbaum, the mayor of Mexico City and one of the country’s most powerful female politicians.

“I don’t like what López Obrador says about women, but he is giving feminists total freedom to enact feminist policies,” said Marta Lamas, a feminist activist and professor at the National Autonomous University of Mexico.

“The president doesn’t know everything and he doesn’t have to, because he has delegated to specialists,” said Ms. Ochoa. “I identify as a feminist and the president knows perfectly well that the policies I am developing address violence against women.”

Meanwhile, the daily murder of Mexican women continues. Last week, Diana Raygoza, a 21-year-old law student, was found dead in her bed, her body mutilated by 39 stab wounds.

In August, Ms. Raygoza wrote on Facebook that she had just been sexually harassed and followed by a stranger on public transportation, and that no one had intervened. The hashtag #JusticiaParaDiana was trending on Twitter this week as people learned of her death.

“You have no idea how disgusted and uncomfortable I felt,” Ms. Raygoza wrote on Facebook. “Do we have to wait until something more serious happens before people react?”

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