MSCI's broadest index of Asia-Pacific shares outside Japan was up 0.1% in early trade, close to this week's three-year highs, while Japan's Nikkei stock average rose 0.9%.
US markets will closed on Friday for the July 4 Independence Day holiday, so the key monthly jobless report was released on Thursday.
The US Labor Department's figures showed that nonfarm payrolls rose by 288,000 last month and the unemployment rate fell to 6.1%. Employment has grown at more than 200,000 in each of the last five months, the first such streak since the late 1990s.
The Dow Jones industrial average passed the 17,000 milestone and the benchmark S&P 500 rose to within 1% of the 2,000 level.
The jobs data pushed up the benchmark US Treasury yield to a two-month high, which in turn burnished the dollar's appeal. The benchmark 10-year yield stood at 2.641% in Asia, not far from its US close of 2.648% on Thursday, when it rose as high as 2.69%.
The dollar was steady against the yen in early Asian trade at 102.21 yen, holding its gains from the previous session in which it ascended a two-week peak of 102.26 yen and marked its largest daily gain in a month.
The dollar index, which tracks the greenback against a basket of rivals, stood at 80.233, slightly up from late US levels after marking a one-week high of 80.315 in the wake of the jobs report.
Recent economic data had painted a more ambiguous picture of the US growth outlook, and had given investors no reason to believe that the Federal Reserve would be hiking interest rates anytime soon. That had pushed down US Treasury yields and dented the dollar.
"The stronger-than-expected June employment report overshadowed recent Fed dovishness," strategists at Barclays said in a note to clients.
European Central Bank President Mario Draghi sounded a dovish note himself on Thursday at a news conference after the ECB decided to hold interest rates unchanged, adding to pressure on the European currency. Draghi said that risks facing the euro zone economy mean that rates will stay low for an extended period.
The euro slipped slightly on the day to $1.3604, after dropping to a one-week low of $1.3597 on Thursday.
In commodities trading, spot gold was flat on the day at $1,319.90 an ounce after dropping in line with the stronger dollar.
US crude was steady from late US trade at $104.10 a barrel.