MEXICO CITY — Hundreds of women marched on Mexico’s seat of government Monday, some carrying their children, others blowtorches, bats and hammers, prepared for a confrontation they hoped would force the country to tackle rampant violence against women.

The International Women’s Day protest was fueled by anger at President Andrés Manuel López Obrador, who has backed a politician accused by several women of rape in a country that suffers some of the world’s worst rates of gender violence. Despite a rift within the governing party over the issue, Mr. López Obrador has supported the politician ahead of June elections.

As the protesters gathered around the national palace — Mr. Lopez Obrador’s residence and the seat of government — their ire was focused on a metal fence that had been erected to protect the building from being overrun. Women wearing black balaclavas pulled down parts of the barricade as the police fired volleys of flash-bang grenades into the crowd, causing several small stampedes.

At least 62 police and 19 civilians were injured by late Monday evening, according to Mexico City’s security branch.

an average of 10 women were killed in Mexico every day, and there were some 16,000 cases of rape. An investigation by one news site, Animal Politico, found that from 2014 to 2018, only about 5 percent of all sexual assault allegations, including rape, resulted in a criminal sentence.

It is that impunity that has enraged Mexico’s feminists, leading some groups to embrace violence as a tactic to force the nation to pay attention to their demands.

“We fight today so we don’t die tomorrow,” women chanted Monday as they marched across the city to the national palace. Others declared, “The fault is not mine, not because of where I was or what I was wearing.”

Over the weekend, activists spray-painted the barricade around the palace with the names of women killed by their husbands, boyfriends or supposed admirers.

filled the capital’s streets after several grisly assaults against women sparked public outrage, including the killing of a 7-year-old girl who was found disemboweled in a body bag.

A day later, tens of thousands of women stayed home from work in a nationwide strike to protest the violence.

accused of sexual assault by several women. The candidate, Félix Salgado Macedonio, is running for governor in the state of Guerrero, pending a party poll to confirm his candidacy.

On the morning of Monday’s protest, the president again accused conservative groups of co-opting the feminist movement, and claimed that women’s marches had begun only after he took power. He pointed to his own government as a commitment to his struggle for equality, the first cabinet in Mexican history to have half the seats filled by women.

Mr. López Obrador defended the wall his government erected around the national palace. And he said that while he supported the feminist movement, he would not tolerate the violence or the vandalism seen during the women’s march last year.

Ms. Granados and her daughter said the wall felt out of keeping for a president who says he is a man of the people.

“Look, I don’t agree to destroy monuments or damage, right?” Ms. Granados said. “But it is also clear to me that a monument is not worth more than the life of a girl.”

Her daughter, Ms. Puente, piped up.

The wall, she said, “is a contradiction.”

Ana Sosa in Mexico City contributed reporting.