An estimated 20,000 people have protested in Verona against a conference which has brought a global network of anti-gay, anti-abortion and anti-feminist activists to the northern Italian city.

The hosting of the World Congress of Families (WCF), a US coalition that promotes the values of the Christian right, has been especially contentious in Italy as it is supported by the far-right League, a partner in the country’s coalition government. Matteo Salvini, the party’s leader and Italy’s deputy prime minister, spoke at the event on Saturday evening.

He said he was there “to support a festive day with a smile: the right to be a mother, a father and a grandparent”. Salvini pledged not to change Italy’s abortion law, known as Law 194, but said the country needed to reverse its shrinking population. “Italians need to start bringing children into the world. A country that doesn’t make babies is a country that dies.”

The protest was brought together by about 70 rights associations from across the country.

“The only positive thing to come out of this event is that all these groups have come together and Italy is uniting,” said Luisa Rizzitelli, a spokesperson for Rebel Network, a women’s group.

“This is a battle to protect the rights and freedom for all, not just one group. We’re all under threat. This congress is not about religion but political power, and we don’t accept this dangerous regression.”

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The self-declared goal of the congress, which began on Friday and ends on Sunday, is to “restore the natural order”. Speakers have railed against same-sex relationships, “radical feminists” and abortion, which has invariably been described as “murder” and “a crime”. On Friday, rubber gadgets of foetuses were distributed to delegates, alongside a card that read: “Abortion stops a beating heart.” Supporters of the WCF also gathered outside the Gran Guardia Palace, where the event is being held. One woman told La Repubblica newspaper that gay people “need conversion therapy” in order to avoid “going to hell”.

Yuri Guaiana, the campaign manager for All Out, a gay rights’ association, said: “They’ve said terrible things about homosexuality, divorce and contraception, and yet they [those involved with WCF] played the victims, saying we were attacking them simply for defending the family.

“This is why it’s important to protest – to show that Italy is not going to surrender to hate.”

Other speakers have included Brian Brown, the WCF president, who fought against same-sex marriage in the US; Theresa Okafor, a Nigerian activist who likened gay people to the Boko Haram terrorist group; and Lucy Akello, a Ugandan politician who helped pass an anti-gay law that sets life imprisonment as the maximum penalty for homosexuality in Uganda. Among the delegates were Russian Orthodox and Mormon leaders as well as Katalin Novák, the Hungarian minister for family affairs.

The congress was snubbed by the League’s coalition partner, the Five Star Movement (M5S), although one of its senators, Tiziana Drago, rebelled and spoke at the event on Friday despite a party order against any participation.

“M5S is very ambiguous, and because of this we can’t be assured that they will defend rights either,” said Guaiana.

• This article was amended on 1 April 2019. An earlier version incorrectly referred to Italy’s abortion legislation as “Law 94”.