In New York trading at about 3.05pm, the Dow Jones industrial average rose 0.5 percent, the Standard & Poor's 500 Index advanced 0.8 percent, while the Nasdaq Composite Index climbed 1.1 percent. Shares pared earlier gains in afternoon trading.
"Volatility is here to stay for the rest of the fourth quarter because even if the Fed doesn't raise rates next week, it is signalling that there is weakness in the economy," Mohannad Aama, managing director at Beam Capital Management in New York, told Reuters.
Gains in shares of Apple and those of Pfizer, last up 2.3 percent and 2.1 percent respectively, led the Dow higher.
"We've stopped most of the panic about China collapsing and the world falling apart," said Ben Kumar, a fund manager who helps oversee about US$14 billion at Seven Investment Management in London, told Bloomberg. "The next question we have to deal with is: is global growth strong enough to deal with a Fed rate rise?"
The US Treasury drew solid demand for its US$13 billion auction of 30-year bonds.
Shares of Lululemon Athletica dropped, last trading 16.6 percent lower, after the company posted margins that fell short of expectations.
"You've got inventories that are bloated. You've got margins that are collapsing. And the explanation to all that is less clear," Canaccord Genuity analyst Camilo Lyon told Reuters. "What that leads into is now a disbelief in their ability to recapture the margin levels that they've talked about."
In Europe, the Stoxx 600 Index ended the session with a 1.2 percent decline from the previous close. Germany's DAX Index slid 0.9 percent, the UK's FTSE 100 Index fell 1.2 percent, while France's CAC 40 Index dropped 1.5 percent.