(Reuters) - Kroger Co KR.N said on Wednesday it was exploring the sale of its nearly 800 convenience stores as the No. 1 U.S. supermarket operator strengthens its online businesses in a market share war that has intensified since Amazon.com Inc's AMZN.O purchase of Whole Foods.

FILE PHOTO: An isle of a Ralphs grocery store, which is owned by Kroger Co, is pictured ahead of company results in Altadena, California U.S., December 1, 2016. REUTERS/Mario Anzuoni

Kroger shares, which have tumbled 40 percent this year on worries that Amazon could shake up the grocery business as it did with books and electronics, rose 1.2 percent to close at $20.78.

Kroger has 784 KwikShop, Tom Thumb, QuickStop and other convenience stores that generate $4 billion in annual sales.

Kroger is revamping its nearly 2,800 brick-and-mortar supermarkets, lowering prices, bolstering in-store technology and investing in online initiatives under a "Restock" plan aimed at gaining advantages over key rival Wal-Mart Stores Inc WMT.N, discounters Lidl and Aldi, and the newly merged Amazon-Whole Foods.

Chief Executive Rodney McMullen said Kroger had to reinvent itself every decade or so.

“We are in the middle of that reinvention today,” McMullen said at the company’s investor conference.

Kroger hired Goldman Sachs to oversee a strategic review of its business, which could lead to other moves, one analyst said.

“With an increased focus on its core retail food business, (Kroger) is likely to explore options for its other non-core assets,” CFRA analyst Joseph Agnese said in a client note. Kroger also owns some 300 jewelry stores.

Kroger reiterated its 2017 net earnings forecast of $1.74 to $1.79 per diluted share. It projected 2018 identical supermarket sales to be stronger than in 2017, when it saw little impact from the recent major hurricanes.

After pulling long-term forecasts in September, Kroger said on Wednesday it did not see anything that would cause 2018 earnings per diluted share to be below $1.80.

While investors have focused on online sales since Amazon and Whole Foods announced their $13.7 billion merger in June, Kroger does not have a major presence in cities like New York and Boston, where grocery delivery is most popular.

“Customers want to engage with us in multiple ways,” McMullen said.

Kroger, which has been a pioneer in using customer data to tailor store offerings and promotions, will be testing delivery at 200 stores by year-end.

It also is investing in ClickList, an online ordering and curbside pickup service that will be in more than 1,000 stores by the end of 2017. Executives said ClickList was growing rapidly and driving incremental sales.