SAN FRANCISCO — Uber has acquired a majority stake in the grocery delivery start-up Cornershop for an undisclosed sum, the company announced on Friday, as it seeks to build its food delivery business.

The company has looked to expand beyond ride-hailing, particularly since its troubled debut on the public markets in May. Although the growth of its core business has slowed, Uber is building its food and freight delivery businesses, as well as expanding into bicycle and scooter rentals.

Cornershop is active in Chile, Mexico, Peru and Canada, and Uber plans to add other markets, including the United States.

“We’re excited to partner with the team at Cornershop to scale their vision, and look forward to working with them to bring grocery delivery to millions of consumers on the Uber platform,” Dara Khosrowshahi, Uber’s chief executive, said in a statement.