Sophia Chikirou, an LFI MP, lauded Quatennens for his “honesty and self-sacrifice” and asked for the public to leave the couple alone.
Such support sparked criticism among feminists, anti-domestic violence campaigners and fellow politicians in France.
Anne-Cécile Mailfert, the president of the Fondation des Femmes (Women’s Foundation), said Mr Mélenchon should read up about marital violence. “It’s not a conflict, it’s violence,” she wrote.
But some of the harshest reactions came from LFI allies.
Sandrine Rousseau, an MP for the green Europe Écologie Les Verts party, called on Mr Quatennens to withdraw from all public speaking. “Violence against women has many faces, none of them is acceptable,” she said.
Aurélien Taché, her party colleague, even suggested he leave his party’s parliamentary group.
In a statement on Sunday, Mr Quatennens said his wife had not intended to bring legal action or speak to the media. He added that he was unaware of what his wife had told the police but that she had wanted to “leave a trace of our arguments”.
He admitted the couple’s relationship had become “strained” and they were planning to divorce after 13 years together. In one argument, he confessed, he had “seized her wrist” and had taken her mobile phone.
“To get it back, she jumped on my back. I got away and in getting away she hit her elbow,” he wrote. He described an earlier dispute in which “in a context of extreme tension and mutual aggression, I slapped her … I profoundly regret this action and I have said sorry many times”.
A statement from LFI said the party “reiterated its relentless engagement in the fight against violence to women”.