Futures tied to the S&P 500 rose almost 2%, suggesting the benchmark U.S. index will claw back some of the losses it incurred Tuesday. Shares in European health and mining companies helped push the Stoxx Europe 600 gauge up 1.3% after a mixed session for equities in Asia.

Mr. Biden won a string of Super Tuesday victories as moderate Democrats rallied behind him, setting up a showdown with Bernie Sanders in the race. The former vice president’s more centrist policies have appealed to investors who are concerned that Mr. Sanders’s pledges, welcomed by the party’s increasingly aggressive left wing, wouldn’t be favorable for businesses.

“A higher probability of a more centrist Democrat candidate has provided some comfort” for investors, said Hugh Gimber, a strategist at JP Morgan Asset Management. Money managers have been particularly concerned about Mr. Sanders’s policy proposals regarding health care and large technology companies, he added.

U.S. health care stocks jumped ahead of the opening bell in New York and were among the best performers. Anthem and Humana rallied 7.3% in premarket trading, while UnitedHealth Group gained 6.6%. HCA Healthcare rose 5.6%. Cigna rallied 5.7% and CVS Health advanced 4.6%.

“Pharma and managed-care providers will be hit in case Bernie Sanders comes in,” said Sophie Huynh, a strategist at Société Générale.

Mr. Sanders has “the most market-sensitive measures,” Ms. Huynh said, pointing to proposals by Mr. Sanders to increase competition in Silicon Valley through more stringent application of antitrust law and to ban fracking, among other policies.

Investors are also hoping that other central banks and governments will follow the Federal Reserve’s lead in taking action to try to alleviate the economic damage caused by the coronavirus epidemic. The Fed on Tuesday cut its key rate by half a percentage point, the first such move between scheduled policy meetings since the 2008 financial crisis.

“Right now, investors are hoping for some kind of coordinated reaction which involves both monetary and fiscal stimulus,” said Cliff Tan, head of markets research for East Asia at MUFG. Investors think “the cavalry of central banks are coming over the hill with whatever it takes” to limit the economic damage caused by the epidemic, Mr. Tan said.

Yields on government bonds, which have dropped as investors bought safe-haven assets and bet that central banks would reduce interest rates, hovered near record lows. The yield on the 10-year U.S. Treasury fell to 0.983%, from 1.005% at the close on Tuesday, when it had briefly retreated to an all-time low of 0.906%.

Some investors remained cautious about the outlook for stocks as coronavirus continued to spread outside China and disrupt businesses in Italy, South Korea and elsewhere. The virus, which has infected at least 93,160 people and killed more than 3,100, prompted the Fed to shift course on monetary policy and has sparked swings in stock markets world-wide over the past two weeks.

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“It’s going to remain volatile and sustainable rallies are going to be difficult for some time to come,” said Hani Redha, a portfolio manager at PineBridge Investments. “The main thing the market is going to need to see is a peak in the infection rate on the coronavirus, and we’re still some way away from that.”

The Fed acted too soon, as it has limited room to further reduce borrowing costs before hitting negative rates, according to Alex Au, managing director at Alphalex Capital Management, a hedge fund based in Hong Kong. It’s hard to determine how much further markets might sell off, Mr. Au said.

“I am just holding my cash, sitting on the sidelines and waiting for clearer signals,” Mr. Au said.

Australia’s benchmark ASX 200 fell 1.7% to close at a nine-month low, while China’s Shanghai Composite Index climbed 0.6%.