NEW YORK — Wal-Mart Stores Inc. is offering to buy South African retailer Massmart Holdings Ltd. for about $4.25 billion in a bid to jump-start growth beyond its sluggish U.S. business.

A deal would give the world’s largest retailer an opening to expand in South Africa, a fast-growing economy but one that’s troubled by high crime and a 24 percent unemployment rate. It also has a heavily unionized work force.

Wal-Mart has focused on expanding overseas, particularly in emerging markets, but South Africa had not been an area that officials had discussed as a potential opportunity.

“South Africa possesses attractive market dynamics, favorable demographic trends and a growing economy,” executive vice president Andy Bond said in a statement. Wal-Mart has sourced products there but doesn’t have a retail presence, company officials confirmed.

Wal-Mart said it would pay $21.11 per share for Massmart, which has 201.5 million shares outstanding, according to Thomson Reuters.

Massmart is Africa’s third-largest distributor of consumer goods, the leading retailer of general merchandise, liquor and home improvement equipment and supplies and the leading wholesaler of basic foods. Massmart was founded in 1990 and operates chains including Game and Makro.

Shares of Massmart surged above Wal-Mart’s offer to $21.29, or 10.6 percent, Monday. That’s an indication that shareholders are expecting a higher offer, either from Wal-Mart or another bidder. Wal-Mart shares fell 60 cents to $53.48.

Massmart said in a statement that its board will provide a recommendation to shareholders once a firm offer is made. The two companies have entered into an exclusivity period to allow for due diligence and other pre-conditions to a deal.

Wal-Mart’s overseas business makes up about 25 percent of its revenue, generating more than $100 billion in the fiscal year that ended Jan. 31. Last month, the discounter reported second-quarter results were helped by robust global growth in China, Brazil and Mexico.

Massmart, based in Johannesburg, runs 290 stores in 13 countries in Africa, with most in South Africa. It also manages eight wholesale and retail chains under various brand names. Its Game stores, Africa’s largest discount chain, offer predominantly general merchandise and nonperishable groceries for home, leisure and business use.

At a news conference Monday, Massmart CEO Grant Pattison said of Wal-Mart: “They’re, of course, very interested in a strategy that includes the entire African continent and therefore have asked questions of Massmart about our operations outside of South Africa, which, as you know, is in several countries as far north as Nigeria and Ghana and as far east as Tanzania and Mauritius.”

Sean Ashton, an analyst from Johannesburg-based Investec Private Client Securities, said Massmart reported revenue of about $6.7 billion in its last financial results. And its strategy is similar to the Wal-Mart model — big box, warehouse-style retailing, he said.

“South Africa is a country that’s still urbanizing, so we should see a continuing trend of the formal retailers gaining market share from informal ones,” Ashton said.

“This is a visionary thing,” said Richard Hastings, macro and consumer strategist with Global Hunter Securities. “The transformation of South Africa is well under way.” He said he believes South Africa will be where South America is today in about seven to 10 years.

But Brian Sozzi, an analyst with Wall Street Strategies, was skeptical.

“I’m surprised,” Sozzi said. “As a Wal-Mart shareholder, I would have a lot of questions. There seems to be too many moving parts. I think they should be fixing their own business in the U.S. There’s too much confusion over its strategy here.”

Sozzi added that digesting Massmart may be difficult because it has a “huge portfolio of brands.”

And he believes with this deal, Wal-Mart is acknowledging it’s going to be difficult to grow in the United States.