Carla Fendi in 2014. (Jacques Brinon/AP)

Carla Fendi, one of five sisters who transformed the family leather goods business into a luxury fashion house that was one of Italy’s first to win global renown, died June 19 in Rome. She was 79.

The Rome-based fashion house confirmed her death but did not disclose the cause.

Her parents, Edoardo and Adele Fendi, founded the company in 1925 with a store fronting the workshop in via del Plebiscito in Rome’s historic center, but it was with the next generation that it surged to prominence as ready-to-wear took off in Italy.

The five Fendi sisters — Paola, Anna, Franca, Carla and Alda — took control of the family business after their father’s death and opened their first Fendi store in another location in Rome’s historic center in 1964.

A year later they hired a young, German-born designer, Karl Lagerfeld, who helped catapult the Italian brand into global fame by elevating fur from staid symbols of luxury to fashion pieces, acquiring lightness and softness, becoming easier to wear and less pompous.

Carla Fendi, left, and sister Anna Fendi in 2007. (Andreas Solaro)

Under Lagerfeld’s direction, Fendi arguably became the most famous furrier in the world. The brand also helped revolutionize leather handbags in the 1990s, making them softer and less rigid, while Ms. Fendi’s niece, Silvia Venturini Fendi, invented the famed Fendi baguette bag, inspired in shape by the traditional French loaf.

“We said to ourselves: ‘Today women are working. We need to change everything,’ ” Venturini Fendi was quoted by La Repubblica as saying. “No one had yet thought of the cross-body bag, practical, comfortable, soft, light.”

The Fendi fashion house eased up on fur as pressure from animal rights activists diminished the market. While never abandoning completely its heritage, the brand started placing fur as the lining of silk coats, or weaving it into fabric or making patchwork pieces, while putting more emphasis on its accessories along with its clothing lines.

Each sister had her role, and Ms. Fendi, as Fendi president, was long the family business’s public face, becoming known as the “signora della moda,” or “lady of fashion.” The sisters sold to the French luxury group LVMH in a deal that was completed in 2001, and Ms. Fendi maintained her role as president until 2008. She was honorary president until her death.

Even as Milan became the center of Italian ready-to-wear, the Fendis maintained their ties to their native Rome, maintaining their headquarters in the Italian capital and sponsoring the renovation of famed landmarks, such as the Trevi Fountain.

Lagerfeld remains the brand’s womenswear designer, along with his other fashion pursuits at Chanel and his own brand, while Venturini Fendi, daughter of Anna Fendi, is the brand’s creative director.

Her latest menswear collection, for spring/summer 2018, showed Monday, hours before her aunt’s death.

Silvia Venturini Fendi, left, and aunt Carla Fendi in 2005. (Andrew H. Walker)

“For her, nothing was impossible,” Venturini Fendi told RAI state television. “The challenges that she always confronted, also as a pioneer in her field. She always had a love of beauty.”

Besides her contributions to fashion, Ms. Fendi will be remembered for her support of Italian culture, including the Spoleto Festival in Umbria. “Fashion (and culture) have lost a star,” La Repubblica wrote Tuesday. Culture Minister Dario Franceschini remembered her as “a cultivated and sensible woman who was a major patron of the arts.”

Ms. Fendi was long married to Candido Speroni. A complete list of survivors was not immediately available.

— Associated Press