Japan's benchmark Nikkei advanced 0.3% while MSCI's broadest index of Asia-Pacific shares outside Japan gained 0.3%, with Australian stocks and South Korea's Kospi up 0.2% and 0.6%, respectively.
The modest Asian gains compared with Wall Street, which rose to near record highs on Friday on a strong jobs report and some sign of optimism about U.S.-China trade talks, with the benchmark S&P 500 closing within 0.2% of its peak set in late November.
U.S. job growth increased by the most in 10 months in November as the healthcare industry boosted hiring and production workers at General Motors returned to work after a strike, in the strongest sign that the economy is in no danger of stalling.
"This economy is still climbing and shattering the records for longevity," said Chris Rupkey, chief financial economist at MUFG Union Bank. "Right now, the clouds of recession still remain well offshore despite troubled economies elsewhere in the world and a trade war."
Top White House economic adviser Larry Kudlow said on Friday that a Dec. 15 deadline is still in place to impose a new round of U.S. tariffs on Chinese consumer goods, but President Donald Trump likes where trade talks with China are going.
Still, investors think things could change if trade tensions escalate further, especially if Trump goes ahead with planned tariffs on some $156 billion worth products from China from mid-December.
The market has been largely working on the assumption that those tariffs, which cover several consumer products such as cellphones and toys, will be dropped or at least postponed, given that Washington and Beijing agreed in October to work on a trade deal.
Meanwhile, China's exports shrank for the fourth consecutive month in November, underscoring persistent pressures on manufacturers from the prolonged trade war, although growth in imports may be a sign that Beijing's stimulus efforts are working.
U.S. Treasury yields climbed after the strong employment report, with benchmark 10-year notes rising to 1.843%.
The Fed's Open Market Committee (FOMC) kicks off its two-day policy meeting on Tuesday. The central bank is expected to highlight the economy's resilience and keep interest rates on hold in the range of 1.50% to 1.75%.
Analysts said Friday's much better-than-expected jobs report offset mixed signals from recent economic data and validated the Federal Reserve's wait-and-see stance on interest rates after three "insurance cuts" this year.
Oil prices retreated but hovered near recent peaks after OPEC and its allies agreed to deepen output cuts by 500,000 barrels per day in early 2020.
U.S. West Texas Intermediate (WTI) crude slipped 0.4% to $58.94 per barrel, still not far from Friday's 2 1/2-month high of $59.85 per barrel.
In the currency market, the dollar maintained a firm tone on Monday, with the dollar index against a basket of major currencies standing at 97.691 and the euro changing hands at $1.1058, both little changed on the day.
Against the Japanese yen, the dollar was last traded at 108.59 yen, flat on the day.
By Tomo Uetake