BANGKOK, Thailand — Thailand's Central Group is buying the Thai business of fashioned-focused e-commerce site Zalora, a unit of the group said on Wednesday.

"Central Group Online .... has studied the deal and signed the agreement to acquire Zalora business in Thailand," Narumon Wipajaroen, company secretary for Central Group Online, said in a statement.

Zalora Group said in a statement that it was also selling its Vietnam business. A spokeswoman for Central Group declined to comment on the Vietnam business.

The two groups did not give financial details of the deals but a media report said the Thai and Vietnam deals were done at $10 million each.

E-commerce in Southeast Asia has become a focus for consumer firms. China's biggest e-commerce company Alibaba Group Holding Ltd earlier this month announced a deal to buy a controlling stake in Southeast Asian online retailer Lazada Group for about $1 billion.

Central Group, like most major Thai retailers, is looking to expand its e-commerce business to win back customers who increasingly prefer to shop online.

It is controlled by the Chirathivat family, the third-richest in Thailand. The group is among the bidders for French retailer Casino Group's Big C supermarket chain in Vietnam.

Zalora is part of Global Fashion Group, the e-commerce firm backed by Sweden's Kinnevik and Germany's Rocket Internet .

By Amy Sawitta Lefevre, Mununphattr Dhanananphorn and Khettiya Jittapong; editor: Muralikumar Anantharaman.