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

The jitters of recent days also calmed somewhat as Russia managed to stabilize its ruble, if only for now, and oil prices bounced up a bit. As risk aversion ebbed, U.S. bond yields rose and the dollar regained some lost ground.

In Asia, Nikkei futures were pointing to an opening increase of at least 1 percent, while stocks in Australia climbed 1.1 percent. MSCI's broadest index of Asia-Pacific shares outside Japan was flat.

Wall Street

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 up 1.69 percent. The S&P 500 gained 2.04 percent and the Nasdaq 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 policy members kept their outlook for rates unchanged.

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.