The all-cash bid for Potash, if successful, would be the biggest takeover so far this year and reflects BHP’s eagerness to expand into potash, a crucial ingredient in most fertilizers.

Soaring demand for food from the fast-growing economies of the world is expected to trigger a growing need for fertilizers and their ingredients.

BHP Billiton, based in Australia, is offering $130 for each share of Potash, a 16 percent premium to its closing price Monday.

But Potash’s shares, which trade mainly on the New York Stock Exchange, surged 28 percent to $143.17 on Tuesday after news of the bid first emerged, reflecting investors’ expectations that BHP might have to raise its offer to secure sufficient acceptance.

In a news media conference call Wednesday, Marius Kloppers, BHP’s chief executive, declined to say whether his company would be prepared to raise the offer, saying that he believed the bid was “fair and full” and that it offered shareholders “certainty of value.”

BHP shares fell 4.4 percent in Australia on Wednesday as investors fretted about the high cost of the proposed transaction, and Moody’s warned that it was likely to put BHP’s credit rating under review for a possible downgrade if a formal takeover offer was made.

But Mr. Kloppers said he was confident that the cash-rich BHP would be able to preserve a solid A-grade rating.

BHP’s offer to shareholders is scheduled to start formally on Friday and remain valid until Oct. 19, the company announced Wednesday.

“We firmly believe that Potash Corp. shareholders will find the certainty of a cash offer, at a premium of 32 percent to the 30-day trading day period average, very attractive, and we have therefore decided to make this offer directly to those shareholders,” Jacques Nasser, BHP’s chairman and a former chief executive of Ford Motor, said in a statement.

BHP, perhaps best known for its activities in iron ore, aluminum, copper and coal, has been expanding into the generally lucrative market for fertilizers for some time in a bid to tap into a long-term trend for increased demand. It has bought several smaller producers of potash in the Canadian province of Saskatchewan, which has some of the world’s richest deposits of the mineral, and announced tentative plans last year to build a mine there.

Acquiring Potash Corp. would catapult BHP into pole position in the global fertilizer industry while also helping it expand its geographical reach into developed countries and bolster its offerings beyond mining. BHP has also been under pressure from its shareholders to deploy capital and take advantage of its balance sheet, which does not carry a heavy amount of debt.

Potash Corp. rejected BHP’s overture Tuesday, describing it as an effort to exploit a downturn in the fertilizer market.

“This proposal, sorry as it was, has put a very bright, focused light on the value of Potash,” William J. Doyle, Potash’s president and chief executive.

“I’m not saying that we’re opposed to a sale,” he said. “We are opposed to a steal of the company.”

BHP’s giant, unsolicited offer raised hopes that merger and acquisition activity in general might be heading for a revival. But economists and analysts cautioned against assuming that the bid was a clear signal that commodities were finally shaking off the effects of the global recession.

Instead, the interest of the British-Australian miner in Potash has more to do with global changes in food production and the peculiarities of the potash market, they said.

“Fertilizer, and in particular potash, is a particularly unique product,” said Murray Fulton, an economist at the University of Saskatchewan. “What you have in the potash industry are a set of players that are able to control supply and price.”

Rising standards of living and development in China, one of the world’s largest consumers of fertilizer, and in India are putting increasing pressure on farmers to produce more crops from a declining amount of agricultural land. Their most effective solution for increasing yields is commercial fertilizers from Potash and other fertilizer makers.

The mineral “potash, for all intents and purposes, is food,” said Vincent Andrews, the agriculture analyst for Morgan Stanley. “Because without potash, you are not making corn and soybean, and without corn and soybean, you are not making chicken or beef, and that’s what people want to eat.”

Of the three main ingredients in most fertilizers, potash is arguably the most valuable. Of the others, nitrogen is produced from natural gas, and good-quality phosphate deposits are found throughout the world. Potash Corp. produces all three ingredients in various countries.

When food prices spiraled upward in 2007 and 2008, prices for potash also surged. When the global recession hit and food prices sank, many farmers simply stopped using fertilizer or greatly limited its application.

Some analysts have speculated that another mining concern — like Rio Tinto or Vale — may emerge as a rival bidder, though on Tuesday people close to BHP emphasized the strength of the company’s balance sheet and financing commitments.

Any sale of Potash will be politically charged in the company’s home province, Saskatchewan. Royalties from potash mines account for a substantial portion of its government’s revenue.

The company was formed by the provincial government in 1975 when it took over potash mines in Saskatchewan. While it sold its final interest in the company in 1989, provincial law still requires that the company have its headquarters in the province.

Bill Boyd, the province’s minister of energy and resources, said any buyer could fulfill that requirement simply by making the province the headquarters of its potash business.

While Mr. Boyd was confident that the broad public would not demand that Potash remain independent, he had no doubt that there would be controversy.

“Potash and public debate are not all that far apart in Saskatchewan,” he said.

Bettina Wassener reported from Hong Kong and Ian Austen from Ottawa. Michael J. de la Merced and Cyrus Sanati contributed reporting from New York.