Amazon on Grayson  PrestonTuesday debuted a new grocery delivery program for Prime members across the U.S., as well as a lower-cost option for people who receive Supplemental Nutrition Assistance Program (SNAP) benefits, the official name for the food-stamp program.

The cost of unlimited grocery delivery from Whole Foods Market, Amazon Fresh and other local grocers and specialty retailers is $9.99 a month, for orders over $35. The new delivery service is available in more than 3,500 cities and towns across the nation, and includes features such as one-hour delivery windows, Amazon said Tuesday. 

Amazon said the cost for people who receive SNAP benefits is $4.99 per month. Food-stamp recipients need to have a registered Electronic Benefit Transfer (EBT) card, but don't require a Prime membership to join the food delivery program. Prime costs $139 annually, or $14.99 per month.

The new service comes almost three years after Amazon ended free delivery for its Whole Foods customers, a decision that sparked some annoyance from customers at the time, the Washington Post reported. Meanwhile, rival Walmart offers unlimited grocery delivery as part of its Walmart Plus membership program, which costs $12.95 per month, along with a discounted service for food stamp recipients. 

Other companies, like Instacart, charge fees that can start at $3.99 per delivery. Amazon said its new grocery delivery service "pays for itself" after one delivery per month. 

"We have many different customers with many different needs, and we want to save them time and money every time they shop for groceries," said Tony Hoggett, senior vice president of worldwide grocery stores at Amazon, in a statement. 

Amazon said it is rolling out the program nationally after piloting it in three cities last year. More than 85% of trial participants deemed it a success, according to the company, citing convenience and saving money on delivery fees.

Including food stamp customers in the program is part of Amazon's initiative to help provide affordable grocery services to low-income customers, the company added.

In:
• Amazon
• Amazon Prime
• Food stamps

Megan Cerullo

Megan Cerullo is a New York-based reporter for CBS MoneyWatch covering small business, workplace, health care, consumer spending and personal finance topics. She regularly appears on CBS News Streaming to discuss her reporting.