A leading US publishing house, Condé Nast, whose titles include Vogue and GQ, is to stop taking on interns, in a move that signals a further curb on using unpaid labour in the name of work experience.

The publisher is being sued by two former interns at the New Yorker and W magazine, who claim they were paid less than $1 an hour for working up to 14-hour days.

Condé Nast did not confirm the decision, but one of its titles, Women's Wear Daily, reported that the group would end its internship programme next year after current placements had finished.

American law permits employers to take on unpaid interns provided they receive beneficial, educational training and that they are not a substitute for paid employees. But a wave of legal cases has stoked debate over whether interns are being exploited.

In June, a judge ruled that Fox Searchlight Pictures had illegally employed two interns at below minimum wage on the film Black Swan. A former intern's case against Harper's Bazaar is moving through the courts.

The pair suing Condé Nast claim the law was breached because the publisher was gaining an advantage from their labour. Lauren Ballinger, who worked at W magazine in 2009, compared her work there unfavourably with Anne Hathaway's experience in the film The Devil Wears Prada, after she spent days packing accessories for editors. The other, Matthew Leib, said he was paid between $300 and $500 for the two summers he worked for the New Yorker's cartoon archives.

Rachel Bien, the lawyer representing Ballinger and Leib, said it would be "prudent" for Condé Nast to scrap its internship programme: "We've focused on cases where we've seen interns doing real work and not having training or educational experience, and on companies that we feel are most outside of the law."

Bien hoped that the lawsuits would help stamp out abuses. "It's become a practice in certain industries – media and fashion especially – for people to work without pay, and what we're trying to say is, this is not right. Other industries would never do this, so we want to bring these ones into line with the norm."

She said that the Fox case had forced the company to cease using unpaid interns, but paid production assistants at least the minimum wage of $7.25 an hour.

While Bien conceded that internships could play a beneficial role, she said: "Some people feel that they have to exploit themselves to get their foot in the door – and only certain groups are able to work for no pay, more affluent people – so the best-case scenario would be that companies hire interns but pay the minimum wage."