The French-Malian superstar Aya Nakamura, who has been subjected to racist abuse after it emerged that she could perform an Édith Piaf song at this summer’s Paris Olympics, has used a new single to hit back at her far-right critics.

In the track Doggy, released on Friday, the 28-year-old musician sings: “I don’t have enemies, me/It’s them that don’t like me … A load of enemies/But I don’t even know them.”

Nakamura, the most listened-to French-speaking artist in the world, has faced a racist backlash since reports were published suggesting she discussed the possibility of performing a Piaf song when she met the French president, Emmanuel Macron, in February.

The notion that she could sing a song by the iconic 20th-century singer at the Games in July was quickly seized on by the far right in France. “It’s not a nice symbol, honestly, it’s another provocation from Emmanuel Macron,” said Marine Le Pen of the National Rally. Le Pen also complained about Nakamura’s “outfits and vulgarity”.

Mention of Nakamura’s name drew boos from the crowd at a campaign rally in March for the Reconquête party, which is led by far-right former presidential candidate Éric Zemmour.

A small extremist group calling themselves the Natives hung a banner by the River Seine that read: “There’s no way Aya, this is Paris, not the Bamako market.”

Nakamura had already responded on social media: “You can be racist but not deaf … That’s what hurts you! I’m becoming a no 1 state subject in debates … but what do I really owe you? Nada.”

She has also said: “I have the impression that I’ve made you discover Édith Piaf and that she’s reincarnated in me. For the rest, whether they like me or not, that’s their business.”

The Paris prosecutor has opened an investigation into alleged racist abuse against the singer.

France’s culture minister, Rachida Dati, has warned against “pure racism”, and the former footballer Lilian Thuram said: “When people say Aya Nakamura can’t represent France, what criteria do they base it on? I know the criteria, because when I was a footballer, some also said this isn’t the French team because there are too many Blacks.”

The sports minister, Amélie Oudéa-Castéra, has also weighed in, telling Nakamura: “It doesn’t matter, people love you. Don’t worry about anything.”

Born Aya Danioko in Mali, Nakamura arrived in France as a baby. She grew up on a housing estate in the northern Paris suburb of Seine-Saint-Denis with her siblings and mother, who was a griotte, a traditional Malian poet or singer.

Her songs have been streamed 7bn times and last year she sold out three Paris gigs in 15 minutes.

It remains unclear whether Nakamura will perform at the Olympics, but the Paris organising committee is trying to limit the damage from the row. “We are very shocked by the racist attacks against Aya Nakamura,” it has said. “Total support to the most listened-to French artist in the world.”

Agence France-Presse contributed to this article.