Wal-Mart Stores Inc. will announce today it is expanding a program offering $4 prescriptions for some generic drugs to Alaska and 13 more states, two weeks after rolling out the low-cost program in Florida.

The Kodiak Wal-Mart opened its doors today with the new $4 prescription system in its system, ready to go, store manager Carolyn James said.

“It’s just a great, great program,” James said. “We’re really excited about it.”

James said she is making printed lists of prescription drugs included in the initiative available to store patrons, and the list is also available at walmart.com.

“Everything from antidepressants to antibiotics … is on there,” she said. “(The list) will be updated all the time.”

Wal-Mart said it expected to expand the program nationwide when it announced Oct. 5 that it was rolling out the plan in Florida after a successful test in the Tampa area.

Wal-Mart launched the program in what it called an effort to save working Americans money on health care. Critics said it was a stunt to draw in business and a grab for a bigger share of the drug business.

The Florida plan covers a month’s supply of 314 prescriptions. That number is made up of 143 drugs in a variety of dosages and solid or liquid forms.

At the time of the Florida announcement, Minneapolis-based Target Corp., the country’s No. 2 discounter behind Wal-Mart, said it would match its rival’s lower prices in Florida.

Walgreen Co., one of the nation’s biggest drug store chains, said it would not cut prices.

CVS Corp., based in Woonsocket, R.I., referred to a statement it issued when Wal-Mart began the Tampa trial. CVS said at that time that co-pays for most generics were already low and that the chain ‘‘has always provided its customers with very competitive pricing.’’

It is the latest health care initiative by Wal-Mart since late last year, as the nation’s largest private employer seeks to deflect union-backed criticism of its worker benefits.

Health care experts said any price competition is welcome but noted that generics are less of a burden to consumers than higher-priced brand-name drugs that are still under patent.

James, Kodiak store manager, encouraged Kodiak patrons with questions about the new program to contact local Wal-Mart pharmacy technicians.

Wal-Mart said it will host news conferences today with company executives and elected officials in the following states: Alaska, Arkansas, Arizona, Delaware, Illinois, Indiana, Nevada, New Jersey, New Mexico, New York, North Carolina, Oregon, Texas and Vermont.