Wall Street stocks ushered in the first day of trading in the new year with a strong rally as investors were buoyed by a report that showed manufacturing strength in the American economy.

Historically, equities have often traded higher in the opening days of the new year. But after opening with a strong bounce Tuesday, stocks gave back some of their early gains as investors remained skeptical about the strength of the economy and saw a cloudy outlook for the euro zone.

“People are skittish. They’re saying, ‘Show me, show me, show me. Prove it to me, prove it to me, prove it to me,’ ” said Robert Doll, chief equity strategist for fundamental equities at asset-management firm BlackRock.

The Standard Poor’s 500-stock index gained 1.55 percent, or 19.46 points, to close at 1,277.06, after climbing to 1,284.62 in the morning.

The Nasdaq composite index rose 1.67 percent, or 43.57 points, to 2,648.72, and the Dow Jones industrial average increased 1.47 percent, or 179.82 points, to 12,397.38.

Meanwhile, oil prices shot up on growing concerns that Iran could close the Strait of Hormuz in the Persian Gulf to oil tankers if new sanctions are adopted by Western nations. The tensions in the region caused oil prices to jump $4.13, to $102.96 a barrel on the New York Mercantile Exchange.

In stocks, financial firms led the charge higher. Shares of Bank of America, which was one of the worst-performing stocks last year, had one of the biggest moves, rising 4.32 percent, to $5.80. JPMorgan Chase shares climbed 5.2 percent, to $34.98, and Citigroup’s stock jumped 7.68 percent, to $28.33.

Some analysts attributed the early optimism in the day to a new report on manufacturing. The Institute for Supply Management, a trade group of purchasing managers, said its manufacturing index rose to 53.9 points in December from 52.7 in November. Readings above 50 indicate expansion.

Despite the stronger tenor of the report, other analysts remained cautious about drawing broader conclusions.

“The investor base got badly burned this time last year when many who were pessimistic in late 2010 switched to being optimistic in early 2011,” said Cary Leahey, senior economist at Decision Economics.

Investors raised their forecasts for economic growth and “upped their expectations of corporate earnings — and equity performance peaked in the second quarter and growth turned out to be about half of what people had hoped,” Mr. Leahey said.

Joseph Saluzzi, a co-head of trading at Themis Trading, said it was too early to say investors had a new, buoyant resolve. Fairly low trading volumes early in the day did not indicate to him that a flood of sidelined cash was moving into the markets.

“Nothing is really going to change until you start to see some real hard economic numbers that show growth. We’ve seen these sort of inklings before and they haven’t led to much in the past,” Mr. Saluzzi said.

More economic data will be released later in the week, perhaps providing investors with a bit of additional clarity on the strength of the economy late last year. Major retailers are scheduled to release sales data, which will provide a gauge of consumer spending during the holiday season.

And on Friday, the government reports the closely watched employment figures for December. The early consensus in the market was that the economy generated 150,000 jobs during the month. But even if true, some analysts said the market’s reaction could be muted.

“The market is primed for a good report by recent standards, but it will be a mediocre report by historical standards,” said Mr. Leahey.

Forecasts for much of the euro zone this year appear more bleak.

Chancellor Angela Merkel of Germany warned on New Year’s Eve that “next year will no doubt be more difficult than 2011,” as austerity measures across much of Europe put economic growth at risk.

Mr. Doll of BlackRock said most investors believe Europe is going to have a shallow recession and that, should it occur, would not lead to significant fallout for the United States economy.

“But things will be different if somebody can convince us that Europe is going to fall apart or we see the bankruptcy of a major bank there,” he said. “Then that’s not economic contagion, which we could thwart, but financial contagion, which would be much more difficult to deal with.”

Earlier Tuesday, Asian stocks rose. The Hang Seng Index in Hong Kong, on its first trading session of 2012, jumped 2.4 percent and the Kospi index in South Korea rose 2.69 percent. Markets in Japan and mainland China remained closed for the extended New Year’s holiday.

The Treasury’s 10-year note fell 23/32, to 100 13/32, and its yield rose to 1.96 percent, from 1.88 percent late Friday.

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