MSCI’s broadest index of Asia-Pacific shares outside Japan was up 0.55 percent in early trade, having earlier touched its highest level since July 29.
Australian shares were up 0.3 percent and Seoul’s Kospi added 1.3 percent. Markets in Japan were closed for a holiday.
The US and China both said on Friday that they had made progress in talks aimed at defusing their protracted 16-month-long trade war, and US officials said a deal could be signed this month.
But in a morning note, analysts at National Australia Bank sounded a note of caution.
“As much as the US-China trade updates continue to point to a Phase 1 deal looking like a certainty, the contentious issues on whether the US will cancel the planned December tariffs and remove some of the current tariffs in line with China’s demands remains an unknown and if the issue is not resolved then a deal could easily collapse,” they said.
In comments on Friday, White House economic adviser Larry Kudlow said tariffs set to kick in on December 15, which would cover Chinese imports such as laptops, toys and electronics, would remain on the table, and the decision whether to cancel them would be made by US President Donald Trump.
US Commerce Secretary Wilbur Ross told the Bloomberg news agency he is optimistic that a limited trade deal, which US President Donald Trump has termed Phase One, could be reached this month.
Any lingering uncertainty over the outlook for trade talks was not enough to keep the S&P 500 from gaining 0.97 percent and the Nasdaq rising 1.13 percent to fresh record closing highs on Friday.
The Dow Jones Industrial Average rose 1.11 percent.
On Monday, US S&P 500 e-mini stock futures were up 0.15 percent at 3,067.8.
US job growth slowed less than expected in October and hiring in the prior two months was stronger than previously estimated, data from the Labor Department showed on Friday.
Those numbers followed a private survey of manufacturers in China that showed better-than-expected factory activity in October.
Oil prices, which had surged on hopes for a US-China trade deal, were lower on Monday. Global benchmark Brent crude was off 0.49 percent at $61.39 per barrel and US West Texas Intermediate crude was 0.46 percent lower at $55.94.
In the currency market, the dollar was up 0.04 percent against the yen to 108.21, and the euro was unchanged, buying $1.1165.
The dollar index, which tracks the greenback against a basket of six major rivals, was down slightly at 97.215.
Gold was slightly lower as investors moved into riskier assets. Spot gold was trading at $1,512.42 per ounce, down 0.07 percent.