By Anora Mahmudova, MarketWatch

NEW YORK (MarketWatch) -- U.S. stocks wobbled initially but rebounded by Tuesday afternoon as investors shrugged off concerns over sectarian conflict in Iraq and mildly disappointing government data on inflation and housing.

Consumer prices rose sharply in May, while a number of housing starts declined by more than expected. Meanwhile in Iraq, government forces fought with militant rebels, killing 28 ISIS fighters, according to the Wall Street Journal report.

The S&P 500 (SPX) was 5 points, or 0.3%, higher at 1,942.66. The Dow Jones Industrial Average (DJI) added 30 points, or 0.2%, to 16,812.85.

The Nasdaq Composite (RIXF) added 22 points or 0.5%, to 4,342.60. The Russell 2000 (RUT) index of small stocks rallied, adding 11 points, or 0.9%, to 1,178,18, outperforming other benchmarks.

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Liz Ann Sonders, chief investment strategist at Charles Schwab said that even with the tick-up in the inflation rate, it remains below the Fed's target.

"Today's CPI data was slightly higher than expected and did not come to us as a big surprise, but certainly the uptick sparked fears of a possible risk of inflation," Sonder said.

"On the housing starts, while the headline number was disappointing, the less noisy year-over-year trend is still improving. There are more housing starts this year then there were last year and that's a positive," she added.

In economic news, U.S. consumer prices rose sharply in May for the second straight month, prompting fears that the Federal Reserve may begin tightening the monetary policy sooner than the markets are expecting.

Construction on new U.S. homes fell by 6.5% in May and builders trimmed plans for future projects in another sign that a hoped-for spring revival in the housing market remains elusive.

Officials at the Federal Open Markets Committee began their two-day policy-setting meeting.

Read: What brokerages are saying about the FOMC meeting on Wednesday.

In corporate news, Nuance Communications Inc. (SSFT) shares climbed 2.2% after reports on Monday that the speech-recognition software maker had held talks with suitors, including Samsung Electronics Co. and private equity funds. Nuance shares are up over 27% this year so far.

Tesla Motors Inc. (TSLA) shares rose 4.5% building on an 8.8% gain in the previous session over reports about a possible collaboration with its competitors. Tesla shares have climbed 53% year to date.

Shares of Gentiva Health Services Inc. (GTIV) rallied 4.1% after Kindred Healthcare Inc. (KND) sweetened its bid for the home-health and hospice company.

Shares in E-Trade Financial Corp (ETFCD) and Charles Schwab Corp (SCHW) rallied 6.5% and 5.4% respectively with the Senate hearing on whether high-frequency trading hurts the markets.

European stocks rebounded and were set to close with modest gains. Asian stock were mostly lower, but the Nikkei bucked the trend and finished higher.

Gold for August delivery (GCQ4) fell over $10, along with oil prices. The pound fell against the dollar (GBPUSD) after annual inflation in the U.K. slowed to its lowest rate in almost five years, easing pressure on the Bank of England to hike rates. Oil futures were largely unchanged.

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