MEXICO CITY (Reuters) - A group of women outside Mexico City’s main cathedral clashed on Sunday with men protesting abortion who made Nazi salutes, among scuffles that left dozens injured during a protest of tens of thousands of people on International Women’s Day.

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The incidents reflected an undercurrent of anger throughout the day, in which the city government said 80,000 people marched through Mexico City’s historic core to the public square fronting the cathedral and National Palace.

Wearing green bandanas symbolizing support for abortion rights, at least a dozen women ripped down banners describing abortion as femicide and set them on fire.

The male anti-abortion proponents, some of whom had shaved heads and one of whom carried a whip, yelled vulgar slang in return. Mexico has a small ultra-nationalist movement that shares ideology with global hard-right groups.

Elsewhere in the city center, women in black masks and armed with hammers smashed the windshield of a car, overturned a van and burnt doors of buildings.

Despite many protesters urging against violence, city authorities said the day’s clashes left 65 people with injuries, including burns but none life threatening.

Activists said they attended to show outrage over a wave of femicides in Mexico, which have risen 137% over the past five years.

“They’re killing 10 women a day - the ones that we know about - in the country I’ve lived in my whole life, it’s unacceptable,” said preschool teacher Daniela Garcia, 33, who said she was especially upset by the recent kidnapping and murder of a 7-year-old girl.

At the doors to the National Palace where the president lives, activists tossed Molotov cocktails over a contingent of policewomen in riot gear who were among nearly 3,000 female officers deployed during the march.

One of the homemade bombs burst amid a cluster of protesters, setting the pants of a female photographer from newspaper El Universal on fire. The newspaper said she was hospitalized with second-degree burns.

Along the palace walls, graffitied slogans rebuked the government, including, “the president doesn’t care about us” and “misogynist AMLO,” referring to President Andres Manuel Lopez Obrador.

Activists also used hammers to tear down a metal barrier surrounding the Bank of Mexico, and lit a bonfire whose flames and smoke could be seen blocks away from the public square.

Amid the flashpoints, protesters sang the anti-femicide anthem “Song Without Fear” and young women performed a lyrical dance that moved some observers to tears.

Dancer Angelica Trevino, 26, said her jumps and spins were meant to express frustration.

“The moves were full of this helplessness, of this daily life of not being able be at peace,” she said. “It’s something that brings all of us women here today.”