Protests and celebrations were staged across the world to mark International Women’s Day as issues of gender equality and gender violence were highlighted in myriad ways.

In Spain, an estimated six million – reportedly including nuns – took part in a mass two-hour walkout to demand equal pay and rights for women, according to UGT, one of the country’s largest unions. Thousands of women flooded the streets and squares of Madrid carrying placards saying, “Liberty, Equality, Friendship” and “The way I dress does not change the respect I deserve.”

Flags were flown at half-mast on government buildings in Portugal, where a day of mourning was observed for women killed by domestic violence. India’s capital, New Delhi, and the Indonesian capital, Jakarta, were among cities to witness marches demanding an end to domestic violence, sexual attacks and discrimination in jobs.

People take part in a rally in Puerta del Sol in Madrid, Spain. Photograph: Emilio Naranjo/EPA

There were debates, including a global conference in Rwanda on family planning. And there were public holidays, including in Uganda, where the National Young Women’s Dialogue was held in the capital, Kampala. Sessions training men and women from rural villages on child marriage were organised in Tanzania.

Michelle Bachelet, the UN high commissioner for human rights, issued a statement thanking equality campaigners around the world. She said: “Thanks to the tireless work of such human rights defenders in all corners of the globe, in recent decades we have seen remarkable progress with respect to women’s rights.”

In the UK, the Duchess of Sussex joined the singer Annie Lennox, Australia’s former prime minister Julia Gillard, and the model Adwoa Aboah in a panel discussion at King’s College London about issues affecting women, hosted by the Queen’s Commonwealth Trust. Talking about her “bump”, the heavily pregnant duchess revealed she had been inspired by a Netflix documentary on feminism in which someone had described feeling “the embryonic kicking of feminism”. “I loved that,” said Meghan. “Boy or girl, whatever it is, we hope that’s the case.”

Adwoa Aboah, the Duchess of Sussex and Julia Gillard. Photograph: Daniel Leal-Olivas/AFP/PA

But there was implied criticism of the prime minister, Theresa May, after she took just one question from a female journalist following her Brexit speech in Grimsby, compared with five from male journalists. “Only one question from a woman reporter?” a female TV journalist shouted. May replied: “You’ve had answers from a woman prime minister.”

There was a different complexion to the day in Russia, where it is traditional to offer women flowers and chocolates. The Russian army recruitment office in Yekaterinburg celebrated with a photo of ballerinas in floating white posing with servicemen in combats and with machine guns. “The men’s power lies in women’s tenderness and love!” read the caption.

Vladimir Putin celebrates International Women’s Day in Russia by riding horseback with some female police officers. Photograph: TASS/Barcroft Images

Russia’s president, Valdimir Putin, applauded women for managing everything at home and work while staying “beautiful, bright and charming”. He then marked the occasion by posing on horseback with female police officers, asking them: “What does a young woman need to maintain her figure? Three things: a workout machine, a masseuse and a suitor.”