Shares of private equity-backed hospital operator HCA Holdings Inc rose nearly 4 percent in early trading in a strong stock market debut on Thursday, even as the broad market sank.

The shares were trading at $31.14 on the New York Stock Exchange after rising as high as $31.30, above their $30 pricing in an initial public offering on Wednesday.

HCA's IPO was the biggest private equity-backed offering ever in the United States and is likely to encourage a new round of exits this year.

The top U.S. for-profit hospital operator overcame concerns about its high levels of debt and the possible downside from a new U.S. healthcare law, selling more shares than anticipated at the high end of the given price range.

HCA has been public twice so there was a lot of demand and a lot of name recognition, said Jeff Jonas, portfolio manager at Gabelli Health and Wellness Trust Mutual Fund, which bought HCA shares.

HCA is the best in the (hospital) space, he added. It has highest margins, best growth rates, and is in the best states -- Florida and Texas. They are extremely well positioned.

Other publicly traded hospital operators saw their shares fall on Thursday, with a 1.5 percent decline for the broader Standard & Poor's 500 Index. Community Health Systems shares dropped 3.8 percent after some industry experts said a newly public HCA could attempt to outbid Community Health's takeover attempt of Tenet Healthcare .

HCA was taken private in 2006 in a $21 billion deal, excluding debt, that involved Bain, KKR , Bank of America Corp , Citigroup Inc and HCA's founder, healthcare mogul Dr. Thomas F. Frist Jr.

In its IPO, the Nashville, Tennessee-based company sold 126.2 million shares for $30.00 each, raising $3.79 billion. It had planned to sell 124 million shares for $27 to $30 each.

Underwriters on the IPO were led by Bank of America Merrill Lynch, Citi and JPMorgan .

(Additional reporting by Clare Baldwin, editing by Gerald E. McCormick and John Wallace)