The European owners of grocery stores Giant, Stop & Shop and Food Lion said Wednesday they plan to combine, creating what would be one of the largest supermarket chains in the United States.

Ahold, based in the Netherlands, will acquire Belgium-based Delhaize to become the fifth-largest chain of U.S. grocery stores, according to retail research firm Conlumino.

The companies run more than 2,000 grocery stores in the United States, stretching from Georgia to Maine.

The deal comes as sales growth at many supermarkets has slowed or flat-lined and margins have slimmed. Grocery stores are increasingly pitted against growing discount chains like Aldi, Web-based delivery services and retailers such as Target and Wal-Mart that are expanding their grocery businesses.

Industry analysts say the deal isn’t likely to do much to boost the companies’ sales, but it should cut costs.

Ahold and Delhaize are valued at a combined $29 billion, based on their stock prices at the end of trading Tuesday. They expect the deal to be finished in the middle of 2016, pending regulatory approval, and they will take the name Ahold Delhaize. Between the United States and Europe, the two have 6,500 stores with 375,000 employees and 50 million customers per week.

In the United States, Ahold owns Giant, Stop & Shop and the online grocery service Peapod. Delhaize owns Hannaford and Food Lion. Those stores are expected to keep their names.

Executives at Ahold and Delhaize said on a conference call with investors Wednesday that it was too soon to say if they would close stores, but Frans Muller, chief executive of Delhaize, said the two companies don’t have much overlap in the United States. Ahold’s stores are clustered in the Mid-Atlantic, while Delhaize’s are farther north and south.

The companies estimate that they will be able to save about $560 million a year once they’ve been together three years, mostly by having more leverage with suppliers and slimming their overhead.

In a flat market, the companies say that should help them boost their bottom lines. The companies reported combined operating income last year of $2.4 billion on $60.7 billion of sales.

“This merger creates a leading international food retailer with highly complementary portfolios. Its enhanced scale allows us to innovate and act as a market leader,” Ahold chief executive Dick Boer told investors. “Both companies share similar values, heritages and strategies, and we believe that the cultures of both groups are complementary.”

The same trend has led to other recent deals, such as the merger of grocery stores Albertsons and Safeway, said Kurt Jetta, founder of TABS Group, a consumer analytics firm.

Ahold has the upper hand in the deal, with its shareholders taking a 61 percent stake in the combined company. Boer, the Ahold CEO, will be chief executive of the new company, and Delhaize Chairman Mats Jansson will become its chairman.

The companies’ stock prices fell following the announcement. Ahold shares fell 3 percent to $18.25, and Delhaize shares fell 7 percent to $22.83.