All three indexes had been on the cusp of a bear market—a drop of 20% below recent highs—before Tuesday’s rebound.

Big swings hit other markets, too, sending oil prices soaring after their biggest drop since 1991 and U.S. government bond yields off record lows.

To many analysts, the scale of Tuesday’s moves suggested markets are still in the midst of a tenuous recovery that may take days or weeks to fully unfold.

Many took some comfort from government officials’ plans to help offset an anticipated slowdown in economic activity due to the coronavirus epidemic: White House officials are planning to meet with lawmakers to discuss potential measures, including a payroll-tax cut and help for hourly wage earners, while Japan’s government unveiled a multibillion-dollar plan to help businesses that have been affected by the coronavirus. But analysts warn those measures may not be enough to ease investors’ anxieties, especially with health officials suggesting the number of coronavirus cases is likely to continue rising around the world.

“The markets at the moment are very volatile, very broken,” said Sergey Dergachev, a portfolio manager at Union Investment. “The market participants are very nervous, so every headline or signal provided by central banks and politicians and Trump provides some small relief.”

In energy markets, Saudi Arabia and Russia ratcheted up their oil-price war, with Riyadh raising output and Moscow saying it was ready to pump more crude.

The kingdom may not be able to lift output so far in such a short space of time, said Harry Tchilinguirian, head of commodity strategy at BNP Paribas.

“We’ve never seen Saudi Arabia produce on a sustainable basis at 12 million barrels a day,” Mr. Tchilinguirian said. “That’s a tall order to achieve.”

That may in part be why U.S. crude oil recouped some of the previous session’s losses and rose 7.9% to $33.60 a barrel. Still, oil prices remain well below where they started the year.

Elsewhere, the Stoxx Europe 600 jumped 1.9% and government bond yields rose above recent lows. Some analysts warned the moves could reverse if the coronavirus causes more economic disruption on the continent. Italy placed its entire national territory under quarantine, the most dramatic step by any country so far to contain the epidemic.

“The whole of Italy has been locked down,” said Benjamin Schroeder, a rates strategist at ING. “If that becomes the norm in Europe, that too could probably trigger a new test of these levels.”

In the Asia-Pacific region, Australia’s benchmark S&P/ASX 200 index rebounded to close up 3.1%. The Shanghai Composite Index gained 1.8%.

In China, President Xi Jinpingarrived in Wuhan for a surprise visit. This was his first trip to the epicenter of the coronavirus epidemic since the health crisis began, and comes as China reports a steep decline in the number of new cases.

“President Xi’s trip to Wuhan is declaring China has largely brought the coronavirus under control,” said Bruce Pang, head of macro and strategy research at China Renaissance Securities. Mr. Pang said that in turn had helped shore up investor confidence in China’s economic outlook.

The Hang Seng Index in Hong Kong added 1.4%.

“It is quite normal for the market to have a minor revision after the brutal selloff on Monday, but it is far from a rebound,” said Hong Hao, chief strategist at Bocom International Holdings.

The Trump administration’s proposals appeared to reassure investors by suggesting “the government still has measures to contain the damage brought by the coronavirus,” Mr. Hong said. However, many uncertainties remained, including energy prices, and what the U.S. Federal Reserve will do to follow its emergency interest-rate cut last week, he said.