Spain’s far-right Vox party has refused to sign an all-party declaration condemning violence against women, drawing outrage from civil rights groups and embarrassing its allies in the conservative People’s party.

Vox’s refusal to sign the declaration by Madrid city council on Monday meant that for the first time since a landmark 2004 law on gender violence, local authorities in the Spanish capital were unable to issue a joint all-party statement.

In this month’s national election Vox became the third-largest party in the Spanish parliament, after more than doubling its number of seats with its mix of nationalist, anti-Muslim and anti-feminist rhetoric.

Javier Ortega Smith, a member of both Madrid city council and the national parliament, said the declaration on the UN’s International Day for the Elimination of Violence Against Women addressed only one side of gender violence.

In a speech greeted by shouts of anger from the audience in Madrid’s city hall, he condemned what he described as “denialists” on gender violence, adding: “There are also men who suffer violence from women and are killed by their wives.”

Hours later thousands of people took to the streets across Spain to demand that authorities do more to address the issue.

In Madrid, demonstrators brought traffic in the city centre to a standstill, waving signs saying “How many more women must die?” and chanting: “It’s not an isolated case; it’s patriarchy.”

The remarks were also condemned by the mayor of Madrid, José Luis Martínez-Almeida, from the centre-right PP, whose conservative administration with the pro-business Ciudadanos relies on four Vox votes for a majority in the city council. “It is not politics what you have done here today; it is political posturing,” said Almeida.

The PP’s national leader, Pablo Casado, also tried to distance his party from its far-right allies, urging other parties to “join forces to fight against abusers”.

There was an even angrier reaction from civil rights activists, notably Nadia Otmani, head of an association that helps migrant women deal with gender violence.

Otmani, who has used a wheelchair for 20 years after her brother-in-law shot her as she tried to defend her sister, approached Ortega Smith after his speech, saying: “You cannot do this! You cannot play politics with gender violence!”

“Vox came mounting an important challenge to democracy and started with this one,” said the acting deputy prime minister, Carmen Calvo, from the centre-left Socialists.

According to official statistics compiled since 2003, 1,024 women have been killed in Spain by their partners as of 22 October. To date this year, 52 women have been killed.

The latest victim, a woman in Tenerife, was allegedly murdered by her partner on Monday.