MEXICO CITY — Women poured into the streets on Sunday to start a two-day protest and national strike against gender-based violence, in what organizers hope will be a turning point for women's rights in a country disfigured by violence and machismo.

About 80,000 women took part in the march in Mexico City, the local government said, making it one of the biggest in the capital in years. Many wore purple, the color symbolizing International Women’s Day, celebrated throughout the world on Sunday. They waved signs reading, “Fight today so we don’t die tomorrow” and “We are the voice of those who are no longer with us.”

“This is a cry of conscience for our society,” said Itzel Zurita, 32, who sells homemade food in Mexico state. She and a friend, Reyna Ayala, 34, a Walmart worker, said they joined the protest because they were horrified by all the women they knew — including in their own families — who had suffered abuse.

“If we don’t raise our voices, when will they hear us?” Zurita asked.

Protests marking International Women’s Day took place around the world, despite fears of the fast-moving coronavirus outbreak, and a few turned violent. Security forces fired tear gas at women’s marches in Turkey and Chile. Islamist hard-liners threw rocks and shoes at a women’s rally in Islamabad, Pakistan.

In Mexico City, masked assailants tossed Molotov cocktails and sprayed gasoline that sparked fires in a few areas, including near the national palace, authorities said. Thirteen people were taken to the hospital with injuries, while dozens more had minor wounds, the city government said. But the march was mostly peaceful.

The annual demonstration for women’s rights here turned into something of a social uprising this year after a string of gruesome killings. Women took to the streets around the country — from U.S. border cities such as Ciudad Juárez to communities in southern Guerrero state, where indigenous women and peasants joined marches.

In Guadalajara, demonstrators dyed the water in a public fountain red to dramatize the spilling of women’s blood. In Mexico City’s central plaza, the Zocalo, activists stenciled the names of victims of “femicide” — women killed based on their gender — on the pavement.

Perla Acevedo, 32, an art gallery worker in Mexico City, had participated in other feminist protests in the capital. But she was on the verge of tears Sunday as she watched the throngs of women marching toward the presidential residence — students, mothers and daughters, transgender activists.

Acevedo said she was protesting “for everything that’s happening every day.” Mexico’s femicide rate rose about 10 percent in 2019 to 1,010 cases; an average of 10 women are killed per day. Surveys have found a majority of women have been victims of violence at some point in their lives.

Mexicans have been jarred by several barbaric murders in recent months, including the slaying and skinning of 25-year-old Ingrid Escamilla, and the killing of Fátima Cecilia Aldrighett Antón, a 7-year-old who was abducted at school.

“I know change isn’t going to happen overnight,” Acevedo said. “But people are talking about this at their dinner tables, in schools. That’s what counts.”

She and other marchers said they planned to participate in a national women’s strike on Monday. Major corporations, universities, state governments and other employers have thrown their support behind the strike, promising not to dock participants’ pay.

“What I think is happening is a collective awakening,” said Peniley Ramírez, a columnist for the daily El Universal. Women had protested in Mexico and other Latin American countries for years, she said. “But now being a feminist is politically correct. This makes a difference. The fact we see companies also becoming feminists, the politicians saying they are feminists, the intellectuals saying they are feminists — we are winning an ideological battle.”

The movement has turned into a significant political challenge for President Andrés Manuel López Obrador, who has been one of Latin America’s most popular leaders. His approval ratings have slipped as he has responded in what many view as a ham-handed way to the wave of outrage over femicides.

The leftist leader has suggested that Sunday’s demonstration and the women’s strike were engineered in part by his conservative opponents. He’s linked femicide to free-market policies pursued by his predecessors. Initially, he scheduled the launch of a major lottery contest for Monday, before saying “I forgot” it was the day of the women’s strike. He moved it back a day.

“I’m in favor of women’s causes, but I don’t want the separation of men and women,” he told a gathering on Sunday in Zacatecas state.

Ramírez said the president’s attitude further intensified anger over the government’s failure to curb violence against women.

“Many women say, we voted thinking it would be a leftist government, and you’d think, with a cabinet that is half women, that things at least on the level of public discourse would be different,” she said.

Claudia Ramírez, 36, a government economist, was among those propelled into the streets by López Obrador’s remarks.

“The response of this administration leaves a lot to be desired,” she said. “That’s what made me come.”