Amazon Fresh – which has been trying to gain dominance in the grocery sector – is now offering grocery delivery to non-Prime members. 

An initial rollout of Fresh delivery for non-members kicked off Wednesday in a dozen cities across the nation including Austin, Texas; Boston; Charlotte, North Carolina; Portland, Oregon; and San Diego, California. 

Amazon Prime members will still be able to save on grocery delivery fees and through exclusive savings on items in-store. 

The company has said that it remains committed to investing in and growing its grocery offering. This marks the company's latest investment to try and expand its customer base as it competes with other heavy hitters in the space. 

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"We’re always looking for more ways to make grocery shopping easy, fast, and affordable for all of our customers," said Claire Peters, worldwide vice president of Amazon Fresh. 

The move comes just after Amazon CEO Andy Jassy admitted it wasn't as far along as it wanted to be with its Fresh grocery stores, which recently shed some of its workforce as it reevaluated its in-store staffing and operations model. 

Amazon has been seeing success with Whole Foods Market, which is acquired in 2017. Those food stores have "pioneered the organic grocery space," Jassy said. However, he is still trying to figure out a winning formula for the Fresh grocery business. 

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Jassy told analysts during an April earnings call that while the company has tried many ideas, it hasn't yet "found conviction around the format that we want to go expand much more broadly." 

Jassy said the company has a "set of experiments and ideas and concepts" that it's working on at these stores. He is also hopeful that the company will figure it out "over this next year."

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In order to gain an edge over competitors, he further noted that there needs to be a lot of brick-and-mortar locations, which the company has been working on with Amazon Fresh for a few years. 

The company is making progress though. Its physical store sales grew by 7% on an annual basis during the first quarter.