Amazon Fresh is the latest retailer to cut prices to win over inflation-weary shoppers

• Amazon Fresh is cutting prices on about 4,000 products through weekly sales.
• Shoppers will be able to get discounts online and at the retailer's stores.

Amazon is the latest major retailer to cut grocery prices.

The retail giant will drop prices on about 4,000 items — some by up to 30% — at its Amazon Fresh chain, the company told CNN. The discounts will vary by week and apply both at Fresh stores and on the grocer's website. The lower prices will also affect products from national brands as well as those under Amazon's store brands.

"Increasing our weekly deals across thousands of items and expanding the reach of Prime Savings at Amazon Fresh is just one way that we're continuing to invest in competitive pricing and savings for all of our customers – both in-store and online," Claire Peters, worldwide vice president with Amazon Fresh, told CNN.

Prime members continue to get a 10% discount on hundreds of items, Amazon said.

Amazon has built a network of 44 Fresh stores, according to its website. But along the way, Amazon has closed some Fresh stores and canceled some store openings.

Inflation has been pushing food prices higher over the past few years. And while the rate of price increases has stalled, there have been few signs of groceries actually getting cheaper until recently.

Some consumers have even turned to gardening or extreme couponing to save money on food.

Amazon is the latest retailer to cut prices in an effort to encourage shoppers to buy more.

Last week, Target announced it would cut prices on about 5,000 items after it reported its fourth consecutive quarter of same-store sales declines. The price cuts will apply to a range of groceries and personal care items, from frozen pizza to sunscreen.

Walmart also announced similar reductions earlier this month.