In late afternoon trading in New York, the Dow Jones Industrial Average rose 0.23 percent, the Standard & Poor's 500 Index added 0.22 percent and the Nasdaq Composite Index gained 0.54 percent.
Advances in shares of McDonald's and those of Visa, up 1.7 percent and 1.4 percent respectively, propelled the Dow higher.
"Equities offer better value than other asset classes, and so long as the Fed is not overly tight, the bull market will not end. We're nowhere near that level yet," Anastasia Amoroso, global market strategist with JP Morgan Funds in New York, told Reuters.
US Treasuries, however, declined, sliding for a fifth straight day, amid concern the Fed might begin lifting interest rates sooner than anticipated. The Federal Open Market Committee is set to meet next week, on September 16 and 17.
"As we get closer to ending quantitative easing, there's always a risk the Fed comes out and says something a little bit more hawkish," Thomas di Galoma, head of fixed-income rates at ED&F Man Capital Markets in New York, told Bloomberg News. "We're starting to see a bottom in global rates in general."
The greenback benefited from the rise in US yields, with the US currency climbing to a six-year high against the Japanese yen.
"US two-year rates are moving higher, you have the continuing monetary accommodation in Europe and we've had a run of pretty bearish data in Japan," Peter Kinsella, a strategist with Commerzbank in London, told Reuters. "I wouldn't be surprised if we saw dollar-yen at 108-109 quite easily."
Meanwhile, shares of RadioShack plummeted for a second day, last down 11.7 percent at 83 US cents after falling as low as 76.10 cents. Wedbush Securities said on Tuesday the company could file for bankruptcy soon, making the stock worthless by the end of this year, according to Reuters.
In Europe, the Stoxx 600 finished the day marginally lower at 344.7, recovering from a drop of as much as 0.6 percent earlier in the session. France's CAC 40 slipped 0.04 percent, while Germany's DAX fell 0.1 percent. The UK's FTSE 100 Index eked out a 0.02 percent gain.
Bank of England Governor Mark Carney told UK lawmakers that an independent Scotland would need massive currency reserves if it intends to continue using the pound as its currency - somewhere in the range of one year's worth of economic output or about 130 billion pounds.