Luxury fashion powerhouse Prada has acknowledged the ancient Indian roots of its new sandal design after the debut of the open-toe footwear sparked a furore among Indian artisans and politicians thousands of miles from the catwalk in Italy.

Images from Prada's fashion show in Milan last weekend showed models wearing leather sandals with a braided design that resembled handmade Kolhapuri slippers with designs dating back to the 12th century.

A wave of criticism in the media and from lawmakers followed over the Italian brand's lack of public acknowledgement of the Indian sandal design, which is named after a city in the western state of Maharashtra.

Lorenzo Bertelli, son of Prada's owners, responded to the sandal scandal in a letter to a trade group on Friday, recognising their Indian heritage.

"We acknowledge that the sandals... are inspired by traditional Indian handcrafted footwear, with a centuries-old heritage," Bertelli, Prada's head of corporate social responsibility, wrote in the letter to the Maharashtra Chamber of Commerce, seen by Reuters.

The sandals are at an early stage of design, and it is not certain they will be commercialised, but Prada is open to a "dialogue for meaningful exchange with local Indian artisans" and will arrange follow-up meetings, he wrote.

A Prada spokesperson issued a statement acknowledging the sandal's inspiration from India, adding the company has "always celebrated craftsmanship, heritage and design traditions".

Prada products are beyond the reach of most Indians. Its men's leather sandals retail for $844 and up, while the Kolhapuri slippers, sold in Indian shops and street markets, start at about $12.

India's luxury market is small but growing fast, with rising numbers of rich people buying Louis Vuitton bags, Lamborghini cars, luxury homes and watches.

Conversely, Indian culture and crafts are increasingly finding their way into global brand designs. High-end jeweller Bulgari offers a $16,000 Mangalsutra necklace inspired by a chain traditionally worn by married women.

Bertelli's homage to Indian design was sent in response to a complaint from the head of the trade group that represents 3,000 Kolhapuri sandal artisans, as the online uproar gathered momentum.

"From the dusty lanes of Kolhapur to the glitzy runways of Milan... will the world finally give credit where it's due?" India's DNA News posted on X.

Sambhaji Chhatrapati from the Kolhapur Royal family told Reuters by phone he was upset that craftsmen had not been acknowledged for the "history and heritage of 150 years."

Kolhapur-based businessman Dileep More, however, said images of the Prada sandal were bringing cheer to some artisans as they show their traditional product going global.

"They are happy that someone is recognising their work," he said.