NEW YORK (AP) — A rally on Wall Street evaporated after the price of crude oil took a sudden turn lower, deflating gains in the energy sector. Major indexes ended slightly lower Tuesday after being up more than 3% earlier. The market was coming off an even bigger gain of 7% the day before. The rally faded after the price of U.S. oil flipped from a gain to a steep loss of more than 9%. It had otherwise been an ebullient day for markets worldwide following encouraging signs that the coronavirus pandemic may be close to leveling off in some of the hardest-hit areas of the world.

THIS IS A BREAKING NEWS UPDATE. AP's earlier story is below:

A big rally on Wall Street is losing steam in afternoon trading Tuesday, undercut in part by another plunge in the price of oil, but the market is still on track for a rare back-to-back gain.

The S&P 500 was up 0.3% with a half-hour to go in trading, after being up as much as 3.5% in the morning. The market's gains faded as the price of U.S. oil flipped from a gain to a steep loss of more than 9% in the afternoon, which weighed on energy stocks and the S&P 500 overall.

It dampened what had been an ebullient day for markets worldwide, following up on Monday's 7% surge for the S&P 500 on encouraging signs that the coronavirus pandemic may be close to leveling off in some of the hardest hit areas of the world.

Even though economists say a punishing recession is inevitable, the stock market this week has been looking ahead to when economies will reopen from their medically induced coma. A peak in new infections would offer some clarity about about how long the recession may last and how deep it will be.

Investors could then, finally, envision the other side of the economic shutdown, after authorities forced businesses to halt in hopes of slowing the spread of the virus. In the meantime, governments around the world are approving or discussing trillions of dollars more of aid for the economy.

Many professional investors say they've been wary of the recent upsurge and expect more volatility ahead. Those concerns were borne out Tuesday, when the S&P 500 swung up, down, up, down and back up again through the day. It is nevertheless on track to eke out one of the few back-to-back gains for the market since the coronavirus outbreak caused it to start selling off in mid-February.

"We are still in what you would call the relief rally off of the prior low," said Sam Stovall, chief investment strategist at CFRA. He noted that this kind of a rally is common within deep bear markets, Wall Street-speak for when stocks decline 20% or more from a peak.

"There's no guarantee that the worst is behind us, yet traders believe that at least there is some short-term money to be made," Stovall said.

The Dow Jones Industrial Average was up 88 points, or 0.4%, to 22,768, and the Nasdaq was virtually flat, as of 3:24 p.m. Eastern time.

Oil prices have been even more volatile than the stock market in recent weeks as demand dries up for energy amid a global economy weakened by the coronavirus outbreak. Russia and Saudi Arabia have also been locked in a price war, refusing to cut production even as the world is awash in excess oil.

President Donald Trump said last week that he hoped and expected the two sides could agree on production cutbacks, which helped prices spurt higher temporarily. But investors still aren't convinced they can reach a deal, and benchmark U.S. crude oil fell $2.45, or 9.4%, to settle at $23.63 per barrel. Brent crude, the international standard, fell $1.18 to $31.87 per barrel.

Earlier in the trading day, stock markets in Europe and Asia climbed before oil's downward shift.

They rallied after China, the first country to lock down wide swaths of its economy to slow the spread of the virus, authorities reported no new deaths over the past 24 hours. Many experts, though, are skeptical of China's virus figures.

Investors also see signals that the number of daily infections and deaths may be close to peaking or plateauing in Spain, Italy and New York. The number of daily deaths rose in New York, the center of the U.S. outbreak, but other statistics were more encouraging, including the average number of people hospitalized each day.

Experts say more deaths are on the way due to COVID-19, which has already claimed at least 76,000 lives around the world. The U.S. leads the world in confirmed cases with more than 369,000, according to a tally by Johns Hopkins University.

More economic misery is also on the horizon. Economists expect a report on Thursday to show that 5 million Americans applied for unemployment benefits last week as layoffs sweep the country. That would bring the total to nearly 15 million over the past three weeks. Analysts also expect big companies in upcoming weeks to report their worst quarter of profit declines in more than a decade.

Massive aid from the Federal Reserve has helped smooth out snarled trading that had beset lending markets earlier in the sell-off. Companies are coming back to the bond market to borrow, even some with "junk" credit ratings, and investors are actually lending them money again.

Japan's government on Tuesday formally announced a 108 trillion yen ($1 trillion) package for the world's third-largest economy.

In the U.S., the world's largest economy, House Speaker Nancy Pelosi is telling her colleagues that another $1 trillion is needed for the next coronavirus rescue package. Last month, Congress approved a $2.2 trillion package.

In Europe, Germany's DAX jumped 2.8%, and France's CAC 40 rose 2.1%. The FTSE 100 in London added 2.2%.

In Asia, Japan's Nikkei 225 rose 2%, South Korea's Kospi gained 1.8% and the Hang Seng in Hong Kong was up 2.1%.

In a signal that investors are feeling less pessimistic about the economy and inflation, they pushed the yield of the 10-year Treasury up to 0.73% from 0.67% late Monday.

That's still painfully low relative to history. The yield was above 1.90% earlier this year and had never been below 1% until last month. Nonetheless, it's been climbing since it hit a record low of 0.498% in early March, according to Tradeweb.

Despite yields remaining near all-time lows, there is an encouraging sign in bond markets: longer-term Treasury yields are still higher than short-term ones. That's a reversal from the "inverted yield curve" of earlier this year, a warning sign for investors that occurs when short-term yields are higher than long-term ones.

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AP Business Writer Yuri Kageyama contributed.