MSCI's broadest index of Asia-Pacific shares outside Japan ticked up 0.1% in early trade, after falling 0.6% the previous day.
Asian stocks struggled to rebound on Tuesday as investors came to terms with sharply reduced expectations the Federal Reserve will deliver a large interest rate cut at the end of July.
Those views were bolstered after solid gains in US jobs for June and pushed down Wall Street for the second straight day.
MSCI's broadest index of Asia-Pacific shares outside Japan ticked up 0.1% in early trade, after falling 0.6% the previous day. Japan's Nikkei rose 0.5% thanks in part to the yen's retreat against the dollar.
On Wall Street, the S&P 500 lost 0.48% while the Nasdaq Composite dropped 0.78%, led by fall in Apple Inc.
Money market futures are still fully pricing in a 25 basis point cut at the Fed's next policy meeting on July 30-31, but have almost priced out a larger 50 basis point reduction.
"The headline payrolls figures was pretty strong but wages were tepid, so, on the whole, a 25 basis-point cut would be justified as a pre-emptive move and I think the current market pricing is fair," said Naoya Oshikubo, senior economist at Sumitomo Mitsui Trust Asset Management.
Investors' focus is shifting to Fed Chairman Jerome Powell's testimony before Congress later in the week for clues on monetary policy.
In the currency market, fading expectations of aggressive easing by the Fed helped the dollar.
The euro traded at $1.1215, near Monday's low of $1.1207, its weakest level since June 19.
The dollar changed hands at 108.75 yen, having risen up to 108.81 yen in the previous session, its highest in more than a month.
The British pound stood at 1.2518, not far from six-month lows of $1.2481 touched on Friday.
Oil prices were slightly softer as concerns about whether slowing global economic growth would hit oil demand eclipsed tensions over Iran's nuclear programme.
Brent crude futures fell 23 cents, or 0.36% to settle at $63.88 a barrel. US West Texas Intermediate (WTI) crude futures shed 19 cents, or 0.33% to settle at $57.47 a barrel.