The groping of Mexico’s Claudia Sheinbaum by a drunken man has sparked outrage among women, many of whom saw their own fears and experiences reflected in her plight.

“If the president suffered assault with that level of protection and those guards it means that all of us women can be assaulted at any moment,” said Patricia Reyes, a 20-year-old student.

The incident took place on Tuesday while Sheinbaum was walking through a crowd in Mexico City. The man tried to kiss her on the neck and embrace her from behind before she removed his hands and an aide stepped in.

The man was later arrested and Sheinbaum said on Wednesday that she would press for charges.

“This is something I experienced as a woman, but it is something that all women in our country experience,” she said in her daily press conference. “If I don’t file a complaint, where does that leave all Mexican women? If they do this to the president, what happens to all the other women in the country?”

Man appears to grope Claudia Sheinbaum in Mexico City street – video

For some women, watching the country’s first female president being groped in public was a personal affront.

“It was really humiliating,” said María Antonieta De la Rosa, a feminist activist and artist. “I felt angry, enraged and impotent.”

The incident touched off particular furore given the high levels of violence faced by women in Mexico, where an average of 10 are killed every day. In the first six months of this year, more than 500 women were murdered because of their gender in a crime known as femicide.

“The issue of assault is like the base level on the violence thermometer and it culminates in femicide,” said De la Rosa. “So living in a femicidal country, the issue of assault is always there.”

The high rates of violence have fuelled the feminist movement, with tens of thousands of women taking to the streets every year on International Women’s Day.

The groping incident prompted indignation across the political spectrum.

“The president lived what thousands of women experience on the street, out in public, at work,” said Patricia Mercado, a congresswoman with the opposition Citizens’ Movement party. “This assault, this touching that is so invasive of our bodies as women.”

Senators from various parties held a press conference on Wednesday condemning the assault against Sheinbaum.

“If this happens to the head of state, to our supreme commander, to our president of the republic, it also happens silently every day to thousands of women in our country,” said Alejandra Arias, a senator with Morena, Sheinbaum’s governing party.

Alicia Gutiérrez, a 40-year-old nurse, is keenly aware of the dangers facing women on public transport: often, she says, men get just a bit too close and once a man started fondling himself in front of her on a bus.

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“I try not to get on public transport that’s too full, or always sit next to a woman,” she said.

When asked about what happened to Sheinbaum, Gutiérrez was indignant. “If being president she was touched in that way, what hope is there for us common folk?”

The incident sparked promises from female politicians of action to protect women from assault.

“The crime committed yesterday against the president of Mexico not only violated her safety, integrity, and dignity, it is called sexual abuse and must be considered a serious crime throughout the country,” said Laura Itzel Castillo, another Morena senator.

“In the coming days, we will meet with the equality commissions across the country to review our legislative agendas and make significant progress in the prevention, response to, and punishment of all forms of violence against women.”

Not everyone in politics showed support. Alejandro Moreno, the head of the opposition PRI party, suggested the incident may have been staged to distract the public from cartel violence.

“It’s the biggest distraction; it’s crude, vile, and hypocritical,” he said. “That’s what Morena does: try to deceive public opinion.”

De la Rosa said the accusation “revictimised” Sheinbaum “because it undermines the victim’s credibility in their own story”.

Sofia Landa, a house cleaner, said the assault must be punished. “Many women suffer this,” she said. “Sheinbaum has the power to deliver justice.”