The Fed indicated it will end its bond purchases in October and appeared near agreement on a plan to manage interest rates in the future, according to the minutes.
"The market, after digesting the Fed minutes, came to the conclusion that the bond-buying program ending in October is a sign of economic strength," said Peter Cardillo, chief market economist at Rockwell Global Capital in New York.
"So while it was a bit more hawkish, the conclusion is the economy doesn't need any more crutches."
The major US stock indexes dipped immediately after the release of the minutes but quickly recovered.
The Dow Jones industrial average rose 78.99 points or 0.47%, to 16,985.61. The S&P 500 gained 9.12 points or 0.46%, to 1,972.83. The Nasdaq Composite added 27.57 points or 0.63%, to 4,419.03.
Alcoa Inc was one of the S&P 500's biggest advancers, ending up 5.7% at $15.69 after hitting $15.76, the highest since July 2011. On Tuesday, the US aluminum producer reported adjusted second-quarter earnings and revenue that topped Wall Street's forecasts.
While the former Dow component is no longer considered a market-moving industry bellwether, Alcoa is sometimes viewed as setting the tone for the earnings season because it is one of the first high-profile names to report results.
Wells Fargo & Co, the largest US mortgage lender, will report results on Friday. Wells Fargo's stock went against Wednesday's trend, dipping 0.1% to $52.19. Dozens of closely-watched companies, including Dow components, will release earnings reports next week.
S&P 500 companies' profits are projected to grow 6.2% in the second quarter, according to Thomson Reuters data, down from the forecast of 8.4% at the start of April. Revenue is expected to rise 3%.
The expected growth is "not nothing, but it is nothing to get too excited about," Jeff Kleintop, chief market strategist at LPL Financial in Boston, wrote in a note to clients.
"The growth rate supports our outlook for high single-digit earnings growth in 2014 and further gains for US stocks," Kleintop wrote. "But, despite the big show that is likely to be made over the US earnings season in the coming weeks, it is not likely to be all that different from last quarter."
American Airlines Group shares climbed 4.3% to $41.99 on heavy volume. More than 20 million shares traded during the day, above the stock's 10-day moving average of 16.5 million shares. The company narrowed its second-quarter unit revenue growth forecast, raising the low end and scaling back the high end.
Southwest Airlines Co gained 1.9% to $27.21. Delta Air Lines Inc rose 1.4% to $36.96.
About 5.28 billion shares traded on US exchanges, slightly below the 5.79 billion average in June, according to data from BATS Global Markets.
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