MSCI's broadest index of Asia-Pacific shares outside Japan was up 0.2 percent, though still down 0.7 percent for the week.
Wall Street closed down on Thursday with the Dow Jones industrial average and the S&P 500 both touching roughly two-month lows before paring losses.
Japan's Nikkei stock index edged down 0.1 percent in early trade, up 1.3 percent for the week.
The New York Fed's William Dudley, a permanent voting member of the Fed's rate-setting committee, said there was a strong sense among Fed policymakers that markets were underestimating the probability of policy tightening and that the central bank was on track for a rate hike in June or July.
His comments came a day after minutes of the Fed's April meeting revealed that most policymakers felt a rate increase might be appropriate as early as next month.
Markets were pricing in a 32 percent chance the Fed would raise rates in June, according to the CME FedWatch tool, up from 15 percent on Tuesday. A majority now expect a rate hike at the July meeting.
"The Fed has regained the upper hand here. It has reasserted its ability to hike rates in June," strategists at Brown Brothers Harriman said. "Moreover, the response by the dollar and the interest rate markets suggests monetary policy still matters."
Dudley said on Thursday that he was "quite pleased" investors had apparently increased bets that a rate hike would come soon.
The U.S. dollar has rallied on such bets. The dollar index, which gauges the greenback against a basket of six other major currencies, last stood at 95.300 after rising as high as 95.502 overnight, its loftiest peak since March 29. The index was poised to gain 0.7 percent for the week.
Against the yen, the dollar edged down 0.1 percent to 109.90 , but was still up more than one percent for the week. It had notched an overnight high of 110.39, its highest since April 28, before the sell-off in equities led some investors to seek the perennial safe-haven Japanese currency.
The euro was steady at $1.1201, nursing its drop to a more than seven-week low of $1.1180 overnight. It was down about one percent for the week.
Currencies are likely to be a topic at the G7 finance leaders' meeting in Sendai, northern Japan, on Friday and Saturday. The meeting could expose a rift on issues ranging from currency to fiscal policies within the group of advanced economies.
Continuing fears about supply outages in Canada and Nigeria bolstered crude oil futures even as the prospect of a U.S. rate hike in June prompted some investors to cash out of long positions after their recent gains.
U.S. crude added 0.5 percent to $48.40 a barrel, up nearly five percent for the week, while Brent crude added 0.6 percent to $49.12, up nearly three percent for the week.