In Europe, the Stoxx 600 Index ended the session with a 1.2 percent increase from the previous close. France's CAC 40 Index rose 1.1 percent, the UK's FTSE 100 Index gained 1.2 percent, and Germany's DAX Index advanced 1.6 percent.
"Investors are also being forced back into equities because even after the recent swings there aren't any other options that will give the type of returns that equities do," Paul Nolte, portfolio manager at Kingsview Asset Management in Chicago, told Reuters.
Investors are repositioning before next week's meeting of US Federal Reserve policy makers. After last Friday's US government jobs data, futures market traders predicted about a 20 percent chance the Fed will lift rates, down from about 30 percent before the jobs report, according to Reuters.
"If it were not for this financial market turmoil or these lower oil prices, the Fed would certainly raise rates within this year," Tomohisa Fujiki, the head of interest-rate strategy for Japan at BNP Paribas in Tokyo, told Bloomberg. "The market's view on a rate hike is quite mixed right now, just like the views we're hearing from FOMC members."
There was good news on the euro-zone economy. A Eurostat report showed euro-zone gross domestic product grew more than originally estimated in the second quarter, expanding 0.4 percent in the second quarter from the first. Eurostat also upwardly revised its growth estimate for the first quarter to 0.5 percent.
Commodities markets also rallied overnight with prices for iron ore, copper and Brent crude and spot gold each higher.
While there's a sense that abundant global supplies of most commodities will keep pressure on prices, the recent and sudden drop in prices is seen by some as overdone.