SYDNEY--South African retailer Woolworths Holdings Ltd. bid 2.15 billion Australian dollars (US$2.01 billion) for David Jones Ltd., in a move that could flush out rival offers for the Australian department-store operator.

David Jones said its board is recommending shareholders accept Woolworths's offer of A$4 a share, which represents a 25% premium to David Jones's closing price of A$3.19 on Tuesday. The price is higher than an October proposal by Australian rival Myer Holdings Ltd., which was swiftly rebuffed.

Myer said that, in light of Woolworths's approach, it has withdrawn its proposed "merger of equals," which didn't offer any premium to David Jones shareholders. "We have always maintained a disciplined approach to valuation," Myer said in a statement.

Founded in 1838 by a Welsh immigrant, David Jones claims to be the oldest department store in the world still trading under its original name.

Like other Australian retailers, David Jones has been grappling with weak consumer confidence and competition from overseas online retailers, which succeeded in luring Australian shoppers while the nation's currency soared. David Jones shares have nearly halved over the past five years.

The arrival on the high street of well-known foreign players such as Gap Inc. and Zara also has squeezed margins. The competition is set to intensify, with Sweden's Hennes & Mauritz AB opening its H&M-branded stores in Australia this year.

"I think it's best for David Jones to get taken over by the South Africans," said Simon Marais, managing director of Allan Gray Australia, which owns 5% of David Jones. "In South Africa, there's been a real boom in retail. Stocks there are valued much higher than in Australia, so it's a natural thing to buy elsewhere in the world."

Woolworths--one of the biggest companies on the Johannesburg Stock Exchange--is betting that a takeover of David Jones will give it an edge over U.S. and European rivals, which have faced criticism for stocking their Australian stores with clothes that hadn't sold well during the Northern Hemisphere seasons.

Creating a larger entity also would give the company more sway with suppliers, Woolworths Chief Executive Ian Moir said in a statement.

"The combination will create a leading Southern Hemisphere retailer with meaningful scale, able to leverage common fashion seasonality with enhanced sourcing capability," Mr. Moir said.

Woolworths, which has a market value of 54.59 billion rand (US$5.21 billion), is no stranger to Australian retail. It owns 88% of fashion retail chain Country Road, and sells clothing under the Trenery and Witchery brands. Still, four-fifths of Woolworths's sales come from South Africa.

Despite recent headwinds from online sales and new entrants, Australian retailers are starting to see signs of a revival in spending after Australia's central bank cut interest rates to a record-low 2.5% last year.

David Jones has tried to take on online challengers by beefing up marketing on its own website. The company also has valuable property assets in Sydney and Melbourne that make it an attractive takeover target because they could be sold and leased back to bolster the retailer's balance sheet.

David Jones Chairman Gordon Cairns said the premium offered by Woolworths was too good to ignore. "This is a compelling proposal which represents a significant premium to not only our intrinsic value but also to broker valuations and to recent share prices," he said in a statement.

Write to Ross Kelly at ross.kelly@wsj.com

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