February ISM manufacturing came in at 49.5, about 1 point above expectations and topping January's 48.2 print. However, the figure still remained below the 50 contraction-expansion level.
The uptick in the February report "adds another piece of evidence we're not falling into recession anytime soon," Jeremy Klein, chief market strategist at FBN Securities.
As of the U.S. market close Tuesday, Fed funds futures were pricing in a roughly 60 percent chance of a December rate hike, up from 30 percent on Monday, according to CME Group's FedWatch tool.
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The morning gains in stocks came despite a temporary turn lower in U.S. crude oil futures, indicating "today that's real buying with the ISM and potentially first-of-the-month (positioning)," Klein said.
The S&P 500 generally posts its best two-month gain over the March and April period, with average returns of 2.66 percent, according to Bespoke.
Treasury yields rose after the data, with the 2-year yield hitting its highest in a month near 0.85 percent and the 10-year yield touching a roughly two-week high just above 1.83 percent. Gold turned lower.
The U.S. dollar index pared gains, with the euro at $1.0876 after hitting a fresh low against the dollar, going back to Feb. 1. The yen traded at 113.88 yen against the greenback.
European Central Bank President Mario Draghi said Tuesday in a Reuters report that euro area inflation trends are weaker than expected and the ECB's policy review in March has to "be seen against the background of increased downside risks to the earlier outlook."
In other U.S. economic news, construction spending rose 1.5 percent in January to its highest level since 2007, Reuters said. The Markit manufacturing PMI for February came in at 51.3, up from the flash 51.0 print but down from January's final 52.4 read.
The Atlanta Fed's GDPNow model forecast for first-quarter real GDP growth declined for the second time in five days, falling to 1.9 percent after the morning's construction spending and ISM report.
February auto sales rose about 7 percent from the same period last year, with Autodata reporting an annualized sales rate of 17.54 million. Last year, U.S. auto sales hit a record 17.4 million vehicles, Reuters said.
"We're seeing strength (in stocks) partly because of strong auto sales and that says a lot about the durability of continued consumer spending, which is underappreciated by Wall Street," Bogdanov said.
"As long as job growth continues, as long as wages continue to drift up, as long as that happens, I think we have the ability for auto sales to meet or exceed last year's strong sales," she said.
The key data for the week is the jobs report, due Friday.
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"Oil going up is a good thing. I think it's the spillover from the Chinese central bank cutting the reserve (requirement) ratio, which is encouraging to people since the Chinese index was down dramatically heading into yesterday's open," said Marc Chaikin, CEO of Chaikin Analytics. He also attributed morning gains to beginning-of-month inflows.
"Today's opening is consistent with the fact the market is starting to trade a little better and I think we've shaken off the bad January," he said.
European stocks closed more than 1 percent higher Tuesday, with the German DAX outperforming with gains of 2.3 percent. The auto and parts sector outperformed.
Asian equities ended mostly higher, with the Shanghai composite closing up 1.7 percent after the central bank's reserve requirement ratio cut and worse-than-expected manufacturing data. The yuan's midpoint fix against the dollar was slightly firmer.
Overnight in China, New York Federal Reserve President William Dudley said he sees downside risks to his U.S. economic outlook, an assessment that could flag a longer pause before the Fed's next interest-rate hike than he and his colleagues had earlier signaled, Reuters said.
"I think the market's now chopping around, worrying about when the next Fed move is going to be," said Maris Ogg, president at Tower Bridge Advisors. "That's why we're getting strange reaction to things."
"I don't think the underlying growth rate in the U.S. has changed at all. Of course, the large economic blocs in Europe and China have added some uncertainty to that," she said.
Tuesday is also "Super Tuesday," when 12 states hold contests.
"There's still this sense of unease and I'm a little bit concerned this won't come to an end until the presidential election," Ogg said.