NEW YORK—Subway reached an agreement with a master franchisee to open nearly 4,000 new sandwich shops across mainland China over the next 20 years, it said on Tuesday.

International expansion is a key growth strategy for the privately owned U.S.-based chain, which is in the midst of a turnaround plan that also relies on remodeled restaurants, updated menus, and a splashy marketing campaign.

While it seeks to expand overseas, the company has been closing thousands of U.S. locations amid a host of problems, including over-expansion and discounts that eroded franchisees’ profits.

Even so, Subway’s global comparable sales rose 12.1 percent in the first quarter.

Other companies are also beefing up their presence in China, including Starbucks, which plans to open 3,000 new stores there by 2025.

Subway’s deal with master franchisee Shanghai Fu-Rui-Shi Corporate Development Co. Ltd. (FRS) is the largest such agreement in Subway’s history. FRS is funded by a consortium of private investors, including Asia Investment Capital.

FRS will get exclusive rights to manage and develop all Subway locations in China. The 4,000 new restaurants would be a seven-fold increase in Subway’s current footprint there.

“China is a key market with significant long-term growth opportunity, and we look forward to bringing the Subway experience to even more guests in the region,” Subway Chief Executive John Chidsey said in a statement.

By Hilary Russ