“We are deeply concerned that women will be coerced into diverting milk that they would otherwise feed their own babies,” the Black Mothers’ Breastfeeding Association wrote in an open letter in January. Medolac, which said it was working with the Clinton Foundation and wanted to encourage breast-feeding by making it financially attractive, abandoned its plan.

Defenders of payments say that if companies are going to profit, it is only fair for them to pay the suppliers for their raw material, especially since pumping takes considerable time and effort. (Prolacta, which started paying only last year, was accused previously of not making clear to women that their milk donations were going to a for-profit company). Moreover, they say, the commercialization of breast milk could increase the supply available.

The American Academy of Pediatrics says that because of the “potent benefits of human milk,” all premature babies should receive breast milk, preferably from their mothers, but if not, then from donors. But there is not enough donor milk for that, experts say, partly because many women do not know that they can donate or sell excess milk.

Mr. Elster said Prolacta processed 2.4 million ounces, or 18,750 gallons, of milk last year and aimed to do 3.4 million this year. That compares to the 3.1 million ounces dispensed in 2013 by all 18 nonprofit milk banks that belong to the Human Milk Banking Association of North America. Those milk banks do not pay women for milk but do charge hospitals a few dollars an ounce to cover the costs of screening donors and pasteurizing the milk.