MSCI's broadest index of Asia-Pacific shares outside Japan was up 0.15 percent while Japan's Nikkei rose 0.6 percent.
Markets expect U.S. employment data due at 1230 GMT to show a non-farm payroll increase of about 164,000 and 0.2 percent rise in average wage earnings in May.
The data will be followed by a speech from Federal Reserve Chair Janet Yellen on Monday, the last chance for the Fed to communicate with markets before it begins a blackout period ahead of its policy meeting on June 14-15.
"If we see a job figure that is largely in line with market consensus and if Yellen maintains a positive tone on rate hikes, I think the chances of a rate hike in June is pretty high," said Masahiro Ichikawa, senior strategist at Sumitomo Mitsui Asset Management.
Currently U.S. money market futures are pricing in only about 20 percent chance of a hike in June and 60 percent by July.
In recent weeks global markets have been puzzling over what the Fed would do in the near term as relatively upbeat U.S. data have been eclipsed by a still-sluggish global economy and worries over the risk of Britain exiting the European Union.
The uncertain global backdrop was underlined by the European Central Bank, which on Thursday predicted consumer price growth would remain below target through 2018 as it struggles with cheap energy feeding into the price of other goods and services.
"Markets are pricing in smaller chances of hike partly because of worries about 'Brexit'. That is also something that could influence the Fed," Ichikawa added.
Ahead of two key events, Wall Street shares held firm, with the S&P 500 gaining 0.28 percent to 2,105.26, mostly led by 1.3 percent rises in the healthcare sector.
It now only needs to rise about 1 percent to set a closing record.
Oil prices were also fairly supported, with international benchmark Brent futures settling above $50 a barrel the first time in seven months on Thursday, after the latest drawdown in U.S. crude stockpiles offset OPEC's failure to set a ceiling for its output.
Brent traded at $50.11 in early Asian trade, up 0.2 percent from Thursday's settlement.
U.S. West Texas Intermediate (WTI) crude futures CLc1 settled up 16 cents, or 0.3 percent, at $49.17 a barrel. It had tumbled more than $1 earlier.
OPEC failed to agree a clear oil-output strategy on Thursday as Iran insisted on steeply raising its own production, though Saudi Arabia's new oil minister promised not to flood the market and sought to mend fences within the organisation.
The euro was soft and the German debt yield hit a three-week low of 0.109 percent on Thursday after the ECB gave a cautious economic outlook.
The euro fell to $1.1150 from this week's high of $1.1221 touched early on Thursday.
Against the yen, it fell to a three-year low of 121.065 yen and last stood at 121.39 yen.
The yen hit a two-week high of 108.525 per dollar on Thursday, a move some market players attributed to disappointment over a lack of a clear plan on stimulus from Japanese Prime Minister Shinzo Abe.
The yen tends to strengthen when there is a bad news on the economy because it is often used as a funding currency for investment in higher-yielding riskier assets.