The key index of blue-chip stocks briefly crossed into bear-market territory as U.S. markets plunged in response to the World Health Organization’s declaration that the coronavirus outbreak has become a pandemic, and as doubt emerged about a potential tax cut meant to offset the economic impact.

The Dow Jones Industrial Average rallied hard on Tuesday, partly reversing Monday’s 2,000-point drop, in response to expectations that the government might cut payroll taxes. But Wednesday morning, Sen. Chuck Grassley, chairman of the Senate Finance Committee, said that while a cut should be under consideration, it isn’t currently needed. according to a Bloomberg News report.

“I wouldn't say we ought to do it now, but it’s something you could quickly kick in if needed,” Grassley said. “We’re in the process of analyzing the economic impact of the virus so right now I wouldn’t say it’s necessary.”

Shortly after midday, the WHO made its declaration, underscoring investors’ concerns about the outbreak.

In late afternoon, the Dow was down about 1350 points, or 5.3%. Earlier, it had fallen more than 1,650 points, dropping below 23,641.14, which is 20% below the high set on Feb. 12. A close below that level would mark the start of a bear market.

The S&P 500 had fallen 4.6% and the Nasdaq Composite had dropped 4.5%. The market’s so-called fear indicator, the CBOE Volatility Index, was 14% higher at near 54.

Hong Kong’s Hang Seng Index fell 0.6%. The U.K.’s FTSE 100 Index slipped back, losing 1.4%, after an early gain in response to news that the Bank of England cut short-term interest rates. The surprise move reduced rates from 0.75% to 0.25%.

In Italy, a coronavirus hot spot, the FTSE MIB index rose 0.3%, a rare gainer among European markets.

The number of Covid-19 coronavirus cases in the U.S. has risen above 1,000, making the U.S. the eighth country to pass that line.

Adding to the trouble was news that authorities in Saudi Arabia have instructed Saudi Aramco, the national oil company, to increase its oil-production capacity to 13 millions barrels a day from the current 12 million as the nation seeks to increase its share of the global market by boosting output even as the coronavirus hits demand. The Saudi Press Agency reported that Aramco’s CEO will implement the order to raise capacity as soon as possible.

The price of oil was down by 4.2% to $32.89 a barrel.

The coronavirus continues to roil the travel sector. Hilton Worldwide (ticker: HLT) withdrew its financial forecasts Tuesday evening because of the outbreak.

“With the coronavirus now spreading beyond China and the Asia Pacific region, and the related increase in travel restrictions and cancellations around the world, we believe that the potential negative impact will be greater than our previous estimate,” CEO Christopher Nassetta said in the company’s news release. “We will provide an update during our first quarter earnings call, based on the information we have available at the time.”

Hilton stock was down about 19% year to date as of Tuesday’s close. Shares were down 6.3% in afternoon trading.

Shares of cruise operator Carnival (CCL) were down 11.8% after Tuesday’s 10.5% gain. Alaska Air (ALK) stock fell 4.4% after rising 8.3% on Tuesday.

Goldman Sachs upgraded shares of the pharmaceutical company Sanofi (SNY) to the equivalent of Buy from Hold. Still, shares are down about 2.3%. Sanofi started testing an arthritis drug as a coronavirus treatment, according to The Wall Street Journal.

Mallinckrodt (MNK) stock gained 25%. The company updated investors about its effort to settle litigation over its alleged role in the opioid crisis.

“We are pleased that New York state has joined the already 47 states and territories in supporting Mallinckrodt’s proposed global opioid settlement,” Mallinckrodt chief legal officer Mark Casey said in the company’s news release. “We remain committed to satisfying the terms of the agreement in principle and continuing to work toward achieving that objective.”

Write to Al Root at allen.root@dowjones.com