Scores of Brazilian women have taken to the streets to protect a 10-year-old child who was being persecuted by religious extremists for trying to legally undergo an abortion after allegedly being raped by her uncle.

The girl, from São Mateus, a small town in the south-eastern state of Espírito Santo, was admitted to hospital on 7 August complaining of abdominal pain and doctors confirmed she was pregnant.

The child told police she had been abused by her uncle since age six and had stayed silent out of fear. The 33-year-old man is reportedly on the run.

Brazil’s highly restrictive abortion laws – largely written in 1940 – permit terminations in cases of rape, when the mother’s life is at risk and when the birth defect anencephaly is detected.

Yet despite this, the child was forced to fly more than 900 miles to the north-eastern city of Recife for the procedure, following a highly politicized legal battle which saw one hospital in the girl’s home state refuse to treat her.

When the girl reached the hospital where the termination was to be performed on Sunday afternoon, its entrance had been occupied by far-right anti-abortion activists and politicians who were filmed hurling abuse at hospital staff and the child, and trying to stop them entering.

“When you see a 10-year-old girl being criminalized for terminating a pregnancy resulting from rape and because her life is in danger, it really gives you a sense of how religious fundamentalism is advancing in our country,” said Elisa Aníbal, a Recife-based feminist campaigner.

The activists appear to have discovered the hospital’s location, which was kept secret for security reasons, from a hardcore supporter of Brazil’s far-right president, Jair Bolsonaro.

In an online video, which was later deleted but the Guardian has seen, the pro-Bolsonaro extremist Sara Giromini names the girl and falsely claims authorities had kidnapped her and chartered a private jet to transport her to the termination.

“This is an extremely serious human rights violation!” claims Giromini, brandishing a plastic doll she alleged was the size of the fetus.

Until last year Giromini worked for Bolsonaro’s minister for women, family and human rights, a conservative evangelical pastor called Damares Alves. The two women appear together in a widely circulated campaign video in which Alves boasts: “Sara is more than my comrade in this struggle to defend life and the family – Sara is like my daughter.”

Paula Viana, a pro-choice activist who escorted the girl from Recife’s airport to the hospital, said she had been warned anti-abortion activists lay in wait as they drove there in a taxi. They stopped the car, hid the girl in its boot and smuggled her into the building through a side-door.

“It’s just unbelievable this is happening in Brazil, that part of the population really believes abortion is worse than rape,” said Viana from the women’s rights group Curumim. “But we weren’t surprised because we know we have a president who is supportive of these shows of hatred.”

As word of the anti-abortion ambush spread among Recife’s feminist community, activists flocked to the hospital to defend the girl’s right to a termination she had requested.

“We realized we needed reinforcements,” said Aníbal, from the Fórum de Mulheres de Pernambuco group, who summoned supporters on social media.

“By the end of the day there were more than 150 people there supporting that girl … women, trans people, black people, young people … and when we looked at the other group they were mostly old white men in suits, with just few women among them.”

Footage that went viral on social media showed the women challenging the fanatics with a call-and-response battle cry that recalled the Chilean anti-rape anthem A Rapist in Your Path.

“This child fell pregnant after being raped and these fundamentalists are here to say that her life doesn’t matter,” the women chanted. “We’re here to say that our lives do matter.”

Debora Diniz, a reproductive rights campaigner who has championed the girl’s cause, said she had been moved by the “beautiful” rally.

Diniz, who lives in exile because of death threats, called Sunday’s standoff the perfect portrait of Bolsonaro’s Brazil: a “hurricane of hatred” colliding with determined, non-violent feminist resistance.

Gabriela Rondon, a lawyer from the pro-choice group Anis, said the extremists’ widely condemned behaviour had inadvertently boosted the debate about decriminalizing and legalizing abortion.

“Brazil’s laws are clearly inadequate and put millions of women at risk. According to our figures half a million women must subject themselves to illegal abortions each year,” Rondon said. “That’s almost one woman per minute.”

Despite the horrific circumstances, Rondon said Sunday’s demonstration “brought us real encouragement”. “A crowd of women protecting a young girl – it gives us such great hope of change.”

Viana said the girl had said she was desperate to get back to playing football. “She is very strong – but she is just a child … She will need long-term psychological support. She understands everything that she is going through.”

In the US, Rainn offers support at 800-656-4673 or by chat at www.rainn.org. In the UK, Supportline can be reached at 01708 765200. In Australia, support is available at 1800Respect (1800 737 732) or 1800respect.org.au. Other international helplines can be found at ibiblio.org/rcip/internl.html.