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The MSCI's broadest index of Asia-Pacific shares outside Japan was up 0.2%, after tumbling 1.5% on Thursday for its sharpest one-day slump in seven months.
Upbeat comments from the central bank governor helped Australian shares jump 0.9%, with investors buying back after stocks slumped 2.3% for their biggest one-day fall since May in the previous session.
South Korean shares opened down 0.4% while Tokyo's Nikkei stock average opened 0.6% lower.
Most risk assets slid to 2013 lows on Thursday with sentiment rattled by market talk of a hedge fund liquidating big positions in commodities, as well as worries the Fed could prematurely wind down its bond buying programme.
The sharp fall came as many markets had been advancing to their highs, bolstered by receding worries about the euro zone's debt crisis.
"Financial markets appear to be at a transitional point. Following on from the 'Great Moderation' and the 'Great Recession', there now seems to be a debate over the next 'Great' theme," Barclays Capital said in a research.
US Treasuries prices rose on Thursday following several data pointing to slow economic growth, such as weekly jobless claims and factory activity, which underscored the need for the Fed's monetary stimulus.
The euro zone's blue-chip Euro STOXX 50 index fell to a fresh 2013 low on Thursday as unexpectedly weak business activity indexes dampened hopes for the euro zone to soon emerge from recession.
The euro steadied around $1.3187 after falling to a six-week low of $1.31615 on Thursday, and was trading up 0.1% to 122.85 yen after hitting a three-week trough of 122.25 yen on Thursday.
Sentiment towards Europe was also hurt by uncertainty ahead of Italy's election over the weekend. Most investors expect a centre-left government to win and continue with reforms to tackle Italy's debt problems. But a resurgence of former leader Silvio Berlusconi has raised new worries.
The dollar hit a 5-1/2-month high against a basket of currencies on Thursday, a day after minutes from the Fed's last meeting bolstered expectations the central bank may pull back from its bond-buying program sooner rather than later.
Caution remained over the US fiscal woes, with President Barack Obama and top Republican lawmakers so far failing to reach a deal to avert "sequestration" cuts that are set to kick in on March 1, which economists warn would hurt the economy and lead to job losses.
US crude was up 0.2% to $93 a barrel.
