SINGAPORE — From this concrete warehouse perched on the edge of a potentially vast new market for online shopping, the Alibaba Group of China hopes to beat Amazon one head of lettuce at a time.

Under the glare of fluorescent lights, green-vested workers carefully wrap fruit, cheese and other perishables for delivery by vans to a growing group of Singaporeans who prefer to do their shopping online. On a nearby wall, printouts show the sorts of defects that customers have complained about in the past: overripe avocados, smelly spinach, rotten honeydews.

“It’s getting better and better,” said Vikram Rupani, president of RedMart, an online grocery company based in Singapore that is part of Alibaba’s push into the region, “but it’s a continuous process that never ends.”

Alibaba and Amazon already dominate the business of selling stuff online in their home markets. Increasingly, they are competing against each other on neutral ground.