European stocks were the strongest performers after being closed for holidays on both Christmas and Dec. 26.
European investors appeared to be switching preferences from bonds to stocks, as 10-year bond prices dipped but stock markets made solid gains. By mid-session Germany's DAX index had booked a record high, rising 0.8 percent to 9,563.20. Britain's FTSE 100 rose 0.7 percent to 6,743.50 and France's CAC was up 1.0 percent to 4,265.48.
The gains came despite a 2-day rally in the euro that sent it briefly to its highest level since 2011 after German ECB representative Jens Weidmann was quoted by newspaper Bild as saying that weak inflation alone is no reason to keep interest rates low.
In the U.S., where indexes hit records Thursday, they appeared set for further modest gains Friday.
After a 0.8 percent gain to 16,479.88 Thursday, Dow Jones Industrial Average index futures set to gain 15 points at the start of Friday's session. The index has jumped 25.8 percent in 2013, and is on pace to have its best year since 1996. The S&P 500 was due to open a single point higher at 1,837.
"US index futures are extending their gains due to yesterday's drop in the number of people claiming unemployment benefits" said IG Markets analyst David Madden. The fall "is further proof that the US economy is growing."
In Asia, Japan's benchmark index hit a five-year high amid growing signs of inflation.
Tokyo's Nikkei index erased early losses to close slightly higher at 16,178.14, after the country's statistics bureau said prices rose 1.2 percent on an annual basis in November — the fastest rate since 2008. The yen weakened to 105 to the dollar, also for the first time since 2008, which should help boost exports.
The Nikkei has now risen more than 50 percent since January 2013.
Hong Kong's Hang Seng index rose by 0.2 percent to 23,231.86, and China's Shanghai composite gained 1.4 percent to 2,199.06, after the Chinese Cabinet said this year's economic growth would be 7.6 percent, down slightly from last year's 7.7 percent. Fears of a sharp slowdown in the world's second-largest economy had fueled market jitters earlier in the year.
The Chinese news rippled through commodity markets, and in London mining giant Rio Tinto was one of the stronger gainers, up 1.6 percent.
"The simple fact is that the Dow Jones Industrial Average has gained 23 percent this year while the growth rate of the economy picked up to 4.1 percent in the fourth quarter," said Neil Mellor of BNY Mellon Global Markets. With U.S. Federal Reserve monetary policy "likely to remain accommodative well into 2015, it could be argued that these trends should continue over the course of 2014."
However, he said he remains cautious about prospects for emerging markets.
South Korea's Kospi index edged 0.2 percent higher to 2,002.20, while Taiwan's Taiex rose 0.6 percent to 8,535.04. The Sensex index on India's Bombay Stock Exchange was up 0.7 percent to 21,219.40.
In foreign exchange markets, the dollar was trading at 104.85 Japanese yen, while the euro was up 0.8 percent to $1.3817.