Thousands of people in cities across Europe marched in pride parades to support LGBT rights on Saturday.

In Rome, thousands of people took to the streets just days after Italy’s new families minister caused a storm by saying homosexual families do not legally exist.

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“It’s very important that we’re here, because we need to respond and show that it’s not true that we don’t exist,” said marcher Andrea. “We’re people who can have families, and when we say family, all we mean is love.”

The coalition government that took power in Italy earlier this month includes the far-right, nationalist League, which has a long history of anti-gay rhetoric.

In an interview with the Corriere della Sera newspaper on 2 June, the new families minister, the League’s Lorenzo Fontana, responded to a question about how his ministry would deal with families with homosexual parents, referred to in Italy as “rainbow families”.

“Rainbow families exist, do they?” he replied, before qualifying his statement by saying that Italian law does not recognise such families.

Facebook Twitter Pinterest A marcher holds up a banner at the Rome pride parade. Photograph: Fabio Frustaci/EPA

Same-sex civil unions have been legal in Italy since 2016, but non-biological parents do not have parental rights. Italian law only allows heterosexual couples access to fertility treatments.

Speaking at the parade, Michela said she travelled from Rome to Denmark to conceive via IVF, and she and her partner now have a seven-year-old daughter.

“These are heavy, hard days,” she said. “It seems like we’re going backwards rather than forwards. It’s really tiring.”

Raffaele and Simone, who are from Rome and have a 14-month-old daughter, said they are tax-paying citizens and should have the same rights as everyone else.

“We have been together for 11 years and we wanted to start a family, so we went abroad, to Las Vegas. We come home with her and the state doesn’t recognise our existence,” Simone said.

Facebook Twitter Pinterest A drag queen in front of the Greek parliament during the Athens pride parade. Photograph: Yannis Kolesidis/EPA

Facebook Twitter Pinterest A couple at the Bucharest pride parade. Photograph: Daniel Mihăilescu/AFP/Getty Images

In Bucharest, some 3,000 people marched through the city centre, with many celebrating a ruling made by the EU’s top court earlier this week.

The European court of justice ruled in favour of Romanian gay man Relu Coman’s right to have his US husband, Robert “Clai” Hamilton, live with him in Romania.

“Clai and I are two people who did not accept discrimination. If more of us did the same, the world would be better,” Coman said at the march.

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Romania does not recognise same-sex marriage and had argued that Hamilton was not entitled to EU residency rights awarded to spouses.

The European court ruling means that same-sex partners of EU citizens have the right to live in any member state whatever their nationality, even in countries that do not recognise gay marriage.

In Warsaw, organisers estimated 45,000 people marched in the annual “equality parade” to protest discrimination not just against LGBT people but also women, ethnic minorities and people with disabilities.

“The situation in Poland is bad because same-sex couples cannot marry or adopt children,” said Alicja Nauman, who was marching with her partner Dominika Wróblewska.

Facebook Twitter Pinterest Marchers in the Warsaw pride parade. Photograph: Czarek Sokołowski/AP

Facebook Twitter Pinterest The Riga pride parade attracted participants from across the Baltic region. Photograph: Toms Kalnins/EPA

Thousands, including members of a LGBT police association, also turned out for the 14th edition of the pride parade in Athens. Since the leftist government took office in 2015, Greece has extended civil partnerships to same-sex couples, authorised sex changes from the age of 15 and legislated for children to be adopted by same-sex partners.

The “Baltic pride” parade in Latvia’s capital Riga included members of the gay community from fellow Baltic states Estonia and Lithuania.

“Latvia is in last place in the European Union when it comes to the rights of LGBT people,” one of the organisers, Kaspars Zalitis, said. “There is no protection against hate crimes, no respect for trans people – that’s why we think this issue is greatly urgent.”

About 30 people protested before the start of the parade in Riga, following a call by a rightwing group for a demonstration against “the promotion of homosexuality”.