Asian stocks rebounded on Wednesday, following a jump in U.S. shares, after the Federal Reserve made an unprecedented pledge to keep interest rates near zero for at least two years, stemming a global equity rout for the time being.

But investors remained wary about implication of the central bank's move -- that it expects the U.S. economy to remain weak far longer than previously forecast -- supporting demand for safe havens such as gold and the Swiss franc.

"Volatility is calming down from an extreme level. Clearly there's going to be considerable concerns still, but the market had got seriously carried away and gone to an extreme of fear," said Greg Gibbs, strategist at RBS in Sydney.

World stock markets had been tumbling since the start of August on fears of a slide back into recession for the United States, reinforced by a downgrade of the U.S. credit rating on Friday, and the ever-expanding euro zone debt crisis.

MSCI's all-country world stock index remained about 17 percent below its May peak on Wednesday, after slipping as far as 20 percent, the generally accepted definition of a bear market, on Tuesday.

Tokyo's Nikkei rose 1.6 percent and MSCI's broadest index of Asia Pacific shares outside Japan rose about 1.7 percent , led by the materials sector, which jumped more than 3 percent .

Wall Street shares posted their biggest one-day gain in more than two years on Tuesday, when the S&P 500 index leapt 4.7 percent.

Against the Swiss franc, the dollar bought around 0.7220 francs , having plunged 6 percent at one stage on Tuesday to a record low around 0.7067.

The dollar dipped to around 77.00 yen , not far from the all-time trough of 76.15 reached in mid-March.

The euro also touched a record low against the Swiss franc at around 1.0075 , before recovering some ground to 1.0384 francs. But the single currency jumped on the dollar to $1.4350 , putting more distance from last week's trough around $1.4054.

Continued strength in the Swiss franc and yen keeps alive the prospect of further intervention by the Swiss and Japanese authorities, after both took steps to weaken their currencies last week.

Gold firmed from late New York levels to around $1,755 an ounce, after striking the latest in a string of records around $1,778 on Tuesday.

U.S. crude oil climbed back above $80 a barrel, rising more than 2 percent to trade around $81.05 CLc1. (Additional reporting by Ian Chua in Sydney; Editing by Ramya Venugopal)