Kroger is Amazon's closest price rival on groceries, e-commerce analyst Profitero has found.

It looked at more than 12,500 products in 16 categories, studying prices on best-selling items available at Amazon, comparing them to Walmart.com, Target.com and Jet.com, as well as the online prices of other leading “specialist” retailers within major product categories.

Profitero’s study finds that, across the categories monitored, Amazon’s prices generally beat other online retailers.

But interestingly, supermarket leader Kroger, and not Walmart, was the closest to Amazon’s pricing in grocery.

"During the period studied, Kroger averaged 1.6% more expensive than Amazon on 156 exactly matched products; Jet was 3.5% more expensive on 133 products; Walmart was 6.2% more expensive on 172 products; Instacart was 10.7% more expensive on 137 products; and Target was 11.6% more expensive on 153 products," Profitero said.

No retailer studied beat Amazon on price in grocery during the period studied.

The news came as Amazon announced it was rolling out free grocery delivery for Prime members, getting rid of its US$14.99 monthly fee for Amazon fresh. Previously, shoppers would opt in to pay fee in addition to the US$12.99 monthly required to access Prime.

The move piles the pressure onto its competitors, who have been struggling to keep up with Amazon's rapid expansion in the grocery delivery space.