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The Fed ended a two-day meeting on Wednesday with a pledge to keep its aggressive policy stimulus despite improvements in the US economy, pointing to still-high unemployment, fiscal headwinds out of Washington and risks from abroad.
Fed Chairman Ben Bernanke said the central bank might slow the pace of its bond buying but only after the labour market showed sustained improvement over a number of months.
"There will be reasonable US economic growth this year and the unemployment rate will drift lower. But neither will be sufficient to induce the Fed to take its foot off the gas. The open-ended QE program is set to run into early 2014 at the very least," said Martin McMahon, economist at Commonwealth Bank.
The MSCI's broadest index of Asia-Pacific shares outside Japan was up 0.2% while Australian shares added 0.5%. South Korean shares opened up 0.5%.
US stocks rose, and European shares broke a three-day losing streak on Wednesday as investors bet on policymakers finding a fix for a Cyprus bailout.
Cyprus considered nationalising pension funds and ordered banks to stay shut till next week to avert financial chaos after it rejected the terms of a European Union bailout and turned to Russia for aid. Crisis talks among the political leadership in Nicosia are set to resume on Thursday.
Markets were also looking to comments by the European Central Bank, which has said it will provide liquidity to Cypriot banks within certain limits.
"Market participants are probably right to expect a resolution of the immediate crisis that does not destabilize broader European and global financial markets," Barclays Capital said of bailout prospects for Cyprus.
"But the shape of such a compromise is not easy to imagine, and until one emerges, investors had better keep an eye or two on the eastern Mediterranean," it said.
Barclays noted there were still risks the euro zone may opt to keep Cyprus on financial lifeline indefinitely, without taking steps to ensure long-run sustainability, or force the island state out of the euro zone.
The dollar was up 0.1% against a basket of major currencies, and the euro stabilised around $1.2937, off a four-month low of $1.28435 hit on Tuesday. The dollar was around 95.92 against the yen.
Japan's Nikkei stock average opened 1% higher. Japanese financial markets were closed on Wednesday for a holiday.
Market reaction was limited to data showing Japanese exports fell 2.9% in February from a year earlier, down for the first time in two months, suggesting a pick-up in global demand and a weaker yen have yet to fully benefit the country's exports.
Traders eyed China's manufacturing sector data due later in the day for clues on the fragile state of recovery in the world's second-largest economy. In February, the survey by HSBC showed factory activity in Asia's biggest economy grew at its slowest pace in four months.
US crude futures fell 0.3% to $93.27 a barrel.
