After a shocking start to the week, U.S. stocks on Tuesday rallied on reports that a government stimulus would help cushion the country from the economic effects of the growing coronavirus outbreak.

The Dow Jones industrial average jumped 1,167 points, or 4.9 percent, recovering more than half its losses from Monday — the blue-chip index’s worst day since the 2008 financial crisis. The Standard & Poor’s 500 and the tech-heavy Nasdaq composite also finished with near 5 percent gains Tuesday. The S&P closed at 2,882, up 136 points. The Nasdaq finished at 8,344, up 394 points. Financial and technology stocks were leading the way for all 11 market sectors in the S&P 500 index.

The market rally came in the final hour of Tuesday’s trading session on word that the White House was making progress on economic measures to help industries and workers hurt by the coronavirus, including plans to cut payroll taxes, relieve hourly workers and offer targeted help for the airline, cruise and hotel industries. Stocks then zipped in and out of negative territory.

“The prospect of some sort of stimulus is a positive ray of light,” said Sarat Sethi of Douglas C. Lane & Associates. “The government is acknowledging the coronavirus and dealing with it. That is removing some of the uncertainty and giving investors relief.”

After weeks of turbulence, U.S. markets plunged to new depths Monday, cratering more than 7 percent on the dual threat of the outbreak’s spread in the United States and the oil price war that erupted between Russia and Saudi Arabia over production targets. The sudden, sharp market drop triggered a halt to trading for 15 minutes.

“Markets are trying to force a policy response — from central banks and from Washington D.C. A basket of more aggressive monetary policy action is coming and how markets respond is the big question,” David Bahnsen, the chief investment officer of the Bahnsen Group, wrote in commentary Monday. “The market will get something resembling ‘zero bound’ very soon, but that is not likely to be effective,” he continued, referring to the Federal Reserve lowering its benchmark interest rate.

Overseas markets also saw a bounce Tuesday, with Japan’s Nikkei 225 closing up 0.85 percent and Hong Kong’s Hang Seng climbing 1.4 percent. European markets finished in negative territory across the board.

Oil prices, which sank 25 percent on Monday to their lowest trading levels since the 1991 Persian Gulf War, bounced back, too. West Texas Intermediate, the U.S. benchmark, jumped 11 percent Tuesday. Brent crude, the international benchmark, gained 10 percent. Energy stocks rallied, with Chevron, BP and ExxonMobil all gaining.

Reuters reported Tuesday that Saudi Aramco planned to raise output to 12.3 million barrels per day in April, flooding crude markets further and threatening U.S. shale operators, whose oil is more expensive to produce. In turn, the move could hurt oil-producing states and make it more difficult for the domestic economy to heal.

Frank Verrastro, the senior vice president at the Center for Strategic and International Studies, said the move by the Saudis and Russians to flood the market has blunted not only the price of oil, but also the global financial markets.

Some analysts have even speculated that oil prices could reach single digits, which would decimate the U.S. shale oil industry and have far-reaching effects on producing countries that cannot get by without healthy per-barrel prices of $50 or higher.

“Egos and miscalculations can lead to a much larger and adverse economic impact, if it’s not corrected,” Verrastro said, adding that the turmoil in oil markets is broad and deep. “Markets don’t like uncertainty, and that’s what is going on today.

“Pretty soon, these oil companies are going to have to report first-quarter earnings,” Verrastro said. “That could jeopardize outstanding bank loans. Then there are unemployment impacts; truckers and tankers are not moving oil. Prices on airlines are down, but no one is flying. We are going to need some signal that Russia and Saudi Arabia can resolve this before things get better.”

The outbreak continues to spread, with more than 100,000 cases worldwide. The director of the World Health Organization called the threat of a coronavirus pandemic “very real.” More than 800 cases have been confirmed in the United States, with the virus present in more than 30 states. The outbreak is responsible for thousands of deaths worldwide, including 28 in the United States.

Italy on Tuesday began a nationwide lockdown, a drastic attempt to contain its outbreak that will affect the lives of 60 million inhabitants. Israel has instituted a quarantine for all arriving travelers, and Japan is moving closer to declaring a national emergency. But as the virus’s grip on Europe and the United States tightens, China is touting its containment practices, with leader Xi Jinping visiting the city of Wuhan for the first time since the virus emerged there late last year.

“Today equity markets sketched a rebound but are still very far away from recovering the losses on the previous days,” Nancy Davis, the chief investment officer of Quadratic Capital, said in an email. “The two main sources of risk are still out there: Coronavirus and the standoff between Saudi Arabia and Russia regarding potential production cuts. It is still unclear what those two risks could bring to global growth and trade. It is hard to call a bottom right now.”

Markets weren’t appeased after the Federal Reserve last week delivered its first emergency rate cut since the financial crisis. The measure seemed to reinforce investor panic rather than quell it.

“We continue to see the market get whipped around as it searches and thrashes looking for some stability,” said Kenny Polcari of SlateStone Wealth. “Do not expect the market to rally straight up from here after the beating it has taken over the past two weeks. Until we get clarity on both the virus and on what the Saudis and the Russians want to do with oil, expect the markets to remain volatile.”

The yield on the 10-year Treasury note, a staple of global finance, remained below 1 percent, although it had climbed from record lows. The yield on the bond is increasing because investors are fleeing stocks for the security of U.S. federal debt, which is one of the safest investments on the planet. As bond prices rise because of demand, yields fall.

Financial managers urged their clients to look past the current maelstrom and instead fix their gaze a decade down the road.

“Investors need to change their mind-set from thinking about the next few weeks to thinking about five to 10 years from now,” said Clark Kendall, the president of Kendall Capital in Rockville, Md. “Do you want to own 10-year Treasurys with a yield below 0.5 percent? In 10 years, a dollar will only be worth less than $1.05. At this time, it is most important to own financially strong companies that can weather this virus. Just like humans, it is the physically and financial weak that are most at risk. ”