MSCI's broadest index of Asia-Pacific shares outside Japan climbed 0.3 percent. South Korea's Kospi rose 0.7 percent, while Japan's Nikkei dipped 0.1 percent on the yen's gains against the dollar.

Wall Street shares inched higher in a choppy session overnight following the Fed's statements, with the Dow rising 0.17 percent and S&P gaining 0.2 percent.

After a closely-watched two-day meeting, the Fed said the economy was likely strong enough to support an interest rate increase by the end of the year. But it lowered its expectations for 2015 economic growth because of a weak start to the year and reduced its growth and federal funds rate forecast.

The Fed's stance disappointed those in the financial markets who had expected the central bank to signal a rate hike at an earlier juncture like September.

U.S. Treasury yields, which had reached eight-month highs last week, promptly fell. Lower debt yields weighed on the dollar, which dropped against a wide range of its peers.

The dollar index was down 0.1 percent at 94.172 after losing 0.8 percent overnight. The dollar was steady at 123.55 yen after sliding off an overnight high of 124.465 while the euro edged up to $1.1365, adding to the previous day's 0.8 percent rise.

"Expectations were high going into the monetary policy announcement and unfortunately for dollar bulls hoping for a sharp upside breakout, (Fed Chair) Janet Yellen failed to deliver," Kathy Lien, managing director of FX Strategy for BK Asset Management, wrote.

"Investors were hoping for a clear road map for lift off but she did not even mention that the chance of a September rate hike has strengthened."

It was a different story for sterling, which soared overnight after robust British wage growth data supported the case for a rate hike by the Bank of England.

The pound hovered near a seven-month high of $1.5848.

In commodities, Brent crude dipped 0.1 percent to $63.79 a barrel after edging up overnight thanks to a weaker dollar.

Spot gold, another beneficiary of the greenback's weakening following the Fed meeting, was up 0.3 percent at $1,184.98 an ounce.

By Shinichi Saoshiro