American stocks rallied after HCA Inc. agreed to the biggest buyout ever and drugmakers Merck & Co. and Schering-Plough Corp. reported quarterly profits that exceeded analysts’ estimates.

The Nasdaq Composite Index had its best performance this month after ATI Technologies Inc., the no. 1 maker of graphics chips for notebook computers, became a takeover target. Advanced Micro Devices Inc.’s bid for ATI and the proposed acquisition of HCA, the largest American hospital chain, helped the market rebound from a twoday slide.

“There’s a continuation of very vibrant mergers and acquisition activity along with the reemergence of two or three health care stocks,” such as Merck, said Ted Parrish, who helps manage $1.2 billion at Hennsler Financial Group in Marietta, Ga.”That’s a reason for the market to perk up.”

The Standard & Poor’s 500 Index added 20.62, or 1.7%, to 1260.91. The Dow Jones Industrial Average advanced 182.67, or 1.7%, to 11,051.05. The Nasdaq gained 41.45, or 2.1%, to 2061.84, led by ATI and its competitor Nvidia Corp.

The acquisitions raised the prospect that future deals will bolster share prices, while earnings from Merck and Schering-Plough helped outweigh concern about shortfalls from Dell Inc. and Intel Corp. that drove stocks lower last week.

The likelihood of more transactions is helping lift stocks as the value of this year’s announced private-equity purchases has already surpassed last year’s total of $265.5 billion, according to data compiled by Bloomberg. So far this year there have been $287 billion of acquisitions by buyout firms.

The S&P 500 had fallen 2.4% this month through July 21 on investor concern that the Federal Reserve’s two years of interest rate increases as well as oil prices that are 28% higher than a year ago may limit future earnings. Reports this week on consumer confidence and new home sales may also offer new evidence that the economy is slowing.

Second-quarter earnings are growing faster than analysts had expected, according to estimates compiled by Thomso n Financial. Analysts expect S &P 500 companies to report a 13.6 percent gain in profit for the period, above their projection of 12.4% at the end of last week and 10.9% at the start of the quarter.

HCA gained $1.61 to $49.48 after it agreed to a $21.3 billion buyout offer from Bain Capital LLC, Kohlberg Kravis Roberts & Co., Merrill Lynch & Co., and HCA co-founder Thomas Frist Jr.

The total value of the sale will be $33 billion, including the buyers’ assumption of $11.7 billion in debt.That would top the $31.3 billion that KKR paid in 1989 for RJR Nabisco Inc. in the biggest buyout ever. Stockholders will receive $51 for each HCA share, 6.5% more than the July 21 closing price.

The HCA transaction may spur additional deals, said Edward Laux, head of listed trading at Cantor Fitzgerald LP in New York.

“It casts a wider net of what companies might be in play and could be pursued and boosts” their market value, he said.