MSCI's broadest index of Asia-Pacific shares outside Japan edged up 0.4 percent in early trade, recovering from an eight-week low touched on Tuesday while Japan's Nikkei rose 1.0 percent.
"I'd think the markets are supported by lack of negative news flows. It's not that we have clear reason to be positive about the global economy but there may be a bit of unwinding in excessively pessimistic bets," said Hirokazu Kabeya, chief global strategist at Daiwa Securities.
On Tuesday, MSCI's broad gauge of global stocks climbed nearly 1.1 percent, its best session in about a month. The U.S. S&P 500 jumped 1.3 percent, tallying its best day in two months.
The index was led by 3.4 percent gains in Amazon to a record high following a bullish analyst report and 5.3 percent rise in Allergan after the U.S. pharmaceutical company posted strong earnings.
In Europe, results from Credit Suisse and jewellery maker Pandora underpinned the market.
Greek shares also hit 2016 highs after euro zone finance ministers offered to grant Greece some debt relief, causing Greek 10-year bond yields to fall below 8 percent for the first time since early December.
Brazil's benchmark Bovespa stock index gained 3.8 percent and the country's currency jumped after impeachment proceedings against President Dilma Rousseff came back on track, fuelling optimism that a new pro-market administration could take over on Thursday.
In the currency market, the yen stayed on the defensive, following two sessions of steep declines after Japanese officials stepped up their warning about intervening to weaken the currency.
The yen fell to 109.28 to the dollar, having slipped 3.4 percent from its 18-month high of 105.55 set on May 3.
The dollar got broad support from comments by a top Federal Reserve official last week, which kept alive otherwise diminishing hopes of a Fed rate hike following soft U.S. payrolls data on Friday.
New York Fed President William Dudley said that it was reasonable to expect the U.S. central bank would raise rates twice in 2016
The dollar's index against a basket of six major currencies rose to a near two-week high of 94.356 on Tuesday and last stood at 94.234, having recovered 2.5 percent from its 16-month low touched Tuesday last week.
The euro traded at $1.1372, after slipping to a low of $1.13585, its weakest since April 29.
Oil prices were supported by crude supply outages in Canada, Nigeria and elsewhere.
Brent crude futures stood at $45.43 per barrel, having jumped 4 percent on Tuesday. U.S. crude futures traded at $44.57 per barrel.