By Anora Mahmudova, MarketWatch

NEW YORK (MarketWatch) -- U.S. stocks rose for a second day in a row Tuesday, with the S&P 500 ending just shy of all-time highs as worries faded that Russia's annexation of Ukraine's Crimea region would lead to further near-term military conflict.

The S&P 500 (SPX) added 13.42 points, or 0.7%, to close at 1,872.25, just 0.3% off its all-time closing high of 1,878.04 set earlier in the month.

The Dow Jones Industrial Average (DJI) advanced 88.97 points, or 0.5%, to 16,336.19, around 1.5% off its all-time closing high from Dec. 31. Microsoft Corp. (MSFT) led Dow gainers and a broad tech rally, jumping 3.9% to finish at its highest level since 2000 on reports its Office suite of software will soon be available on Apple Inc.'s (AAPL) mobile devices.

With tech stocks surging, the Nasdaq Composite (RIXF) jumped 53.36 points, or 1.2%, to 4,333.31.

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Markets rallied on Monday after the European and U.S. sanctions were limited to visa bans and asset freezes. Tuesday's annexation of Crimea, which happened without a prospect of a full-blown invasion, eased investors' fears and allowed them to focus on fundamentals.

Russia's President Vladimir Putin on Tuesday signed a treaty to annex Crimea after an overwhelming majority of its citizens on Sunday voted to leave Ukraine. In his prepared remarks, Putin also said he does not want to partition Ukraine. While that seemed to cheer investors, there were plenty of skeptics who argued that the prospects of further Eastern European turmoil can't be dismissed.

"Of course, when it comes to Vlad the Crimean Impaler, it is all about what he does, not what he says," said Joel Naroff, economist at Naroff Economic Advisors in Holland, Pa., in a note. "Still, investors like soothing tones, so any time he tries to make nice, markets will likely stabilize."

As the events in Russia and Ukraine stole the show, reaction to a pair of economic reports that were in line with expectations was muted. Investors shifted their attention to the Federal Reserve's two-day policy-setting meeting set to conclude Wednesday.

The Fed will release a policy statement and updated economic forecasts on Wednesday afternoon. Chairwoman Yellen is due to hold a news conference after the meeting, the first to be led by her. Analysts expect the Fed will roll out a new low-rate pledge and further tapering of its monthly bond-buying program.

In economic news, construction on new U.S. homes fell slightly in February, but in a sign that work will pick up as the weather warms, builders filed more permits to start new projects -- mainly on multi-dwelling units like condos and apartments. The previous months' number was revised higher. Also: Spotlight on the economy: Is housing construction about to warm up?

Ian Shepherdson, chief economist at Pantheon Macroeconomics wrote housing starts numbers "could have been worse, but single-family permits numbers are worrying."

"The not-so-good news is that all the increase in permits in February was in the volatile multi-family component, while single-family fell for the third straight month to their lowest level since Jan 13. The trend here is clearly downwards, and SF starts are even weaker," he said in a note.

Consumer prices in the U.S. rose slightly in February because of higher food and housing costs, but overall inflation remained quiet, according to the latest government figures.

Among individual stocks, Hewlett-Packard (HPQ) jumped 3.9% after Barclays upgraded the stock to overweight from equal weight. Barclays analyst Ben Reitzes said H-P "could gain share for several quarters" in the low-end server business at the expense of Lenovo which has acquired IBM Corp.'s X86 server business.

GameStop Corp. (GME) shares dropped 3.4% after Wal-Mart Stores Inc. (WMT) said it would allow customers to hand in used videogames in exchange for gift cards, which can be used in its retail stores or online. The change in policy from Wal-Mart Stores could eat away at GameStop's dominance of the $2 billion used videogame market in the U.S.

Shares of FutureFuel Corp.(FF) rose nearly 18% as the biofuels company late Monday reported a more-than-fourfold jump in profit. Hertz, Adobe, Oracle are stocks to watch Tuesday.

Coach Inc. (COH) shares rose 1.6% after Barclays initiated coverage of the stock with 'equalweight' rating.

Oracle Corp. (ORCL) gained 1.6% in regular trading but fell more than 5% in after-hours action after reporting weaker-than-expected fiscal third-quarter results.

In other markets, gold (GCJ4) fell on Tuesday in volatile trading as investors looked ahead to the Fed meeting. Gold lost ground Monday as investors put money back into stocks. The dollar fell versus the Japanese yen (USDJPY), also reversing some of the previous day's moves. Oil prices (CLJ4) rose.

European stocks gained ground rising 0.6%. The Nikkei 225 index largely tracked Wall Street gains from Monday, with that index gaining close to 1%. The Shanghai Composite Index was flat.

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