A program created by a group that organizes farmworkers has persuaded companies like Walmart and McDonald’s to buy their tomatoes from growers who follow strict labor standards. But high-profile holdouts have threatened to halt the effort’s progress.

Now the group, a nonprofit called the Coalition of Immokalee Workers, is raising pressure on one of the most prominent holdouts — Wendy’s — which it sees as an obstacle to expansion.

The Immokalee workers’ initiative, called the Fair Food Program, currently benefits about 35,000 laborers, primarily in Florida. Over the last decade, it has helped transform the state’s tomato industry from one in which wage theft and violence were rampant to an industry with the some of the highest labor standards in American agriculture.

“They’ve already been successful in a measurable way at effectively eliminating modern-day slavery and sexual assault, and greatly reducing harassment,” said Susan L. Marquis, dean of the Pardee RAND Graduate School in Santa Monica, Calif., who has written a book on the program. “Pay is substantially higher for these people.”