Asian share markets rallied on Thursday after U.S.stocks enjoyed their strongest session this year when the Federal Reserve sounded upbeat on the economy and promised to be patient in removing policy stimulus.

The jitters of recent days also calmed a touch as Russia managed to stabilise its rouble, if only for now, and oil prices eked out a rare bounce. As risk aversion ebbed, U.S. bond yields rose and the dollar regained some lost ground.

In Asia, Japan's Nikkei .N225 jumped 2.4 percent, while stocks inAustralia .AXJO climbed 1.8 percent for its best day since late 2013. MSCI's broadest index of Asia-Pacific shares outside Japan.MIAPJ0000PUS lagged with a rise of 0.2 percent.

Wall Street rebounded after three days of declines after the Fed said it would adopt a "patient" approach to raising interest rates.

Equity investors seemed content that any move would be cautious and drove the Dow .DJI up 1.69 percent. The S&P 500 .SPX gained 2.04 percent and the Nasdaq .IXIC 2.12 percent.

Bond investors were less enthused as some had thought the downward spiral in oil combined with low inflation, economic weakness globally and the Russian financial crisis would lead the Fed to push out the likely timing of the first hike.

Instead, Fed Chair Janet Yellen played down the impact of oil and falling inflation expectations, while most policy members still expected hikes to start in 2015.

As a result, Treasuries erased an early rally and yields on two-year paper jumped 10 basis points from the day's trough to stand at 0.617 percent US2YT=RR.

Still, longer-term yields remain low historically, as do market based measures of expected inflation. Data out on Wednesday showed consumer prices fell 0.3 percent in November, the biggest drop in six months, as fuel costs fell.

As a result, investors continue to wager that any tightening will proceed at a snail's pace. Fed fund futures <0#FF:> currently imply a rate of 0.56 percent by the end of 2015, while the median forecast by Fed members is 1.125 percent.

The rise in yields was enough to revive U.S. dollar bulls after a few days of caution and the currency climbed to 118.85 yen JPY= from a low of 116.29 on Wednesday.

The euro retreated to $1.2325 EUR=, after being as high as $1.2515 at one stage on Wednesday, while the U.S. dollar index gained 1 percent for the day .DXY.

The single currency also took a hit when European Central Bank board member Benoit Coeure said there was support on the bank's policymaking council for more action, with sovereign bond purchases the "baseline option".

In commodity markets, oil prices steadied after some wild swings this week. U.S. crude CLc1 was quoted 16 cents firmer at $56.63 having bounced as far as $58.98 on Wednesday.

Brent LCOc1 ended up 63 cents at $60.64, but had been as high as $68.71 at one stage.