Amazon said on Friday that it had agreed to buy the upscale supermarket chain Whole Foods for $13.4 billion, in the online retailer’s latest push into the grocery business.

The deal as the high-end grocer has been trying to fend off pressure from activist shareholders frustrated by a sluggish stock price.

Whole Foods last month unveiled a sweeping overhaul of its board, replacing five directors, naming a new chairwoman and bringing in a new chief financial officer. It also laid out plans to improve operations and cut costs.

Amazon has designs on expanding beyond online retail into physical stores. The company is slowly building a fleet of outlets, and much attention has been focused on its grocery store dreams.

The e-commerce giant is testing a variety of retail concepts. It has opened a convenience store that does not need cashiers, and has explored another grocery store concept that could serve walk-in customers and act as a hub for home deliveries.

Under the terms of the proposed deal, Amazon would pay $42 a share, a 27 percent premium to Thursday’s closing price.