MSCI's broadest index of Asia-Pacific shares outside Japan was up 0.1 per cent, with resource-heavy Australian shares rising 0.6 per cent. The MSCI ex-Japan shed nearly 12 per cent in 2015.
Japan's Nikkei fell 1 per cent, playing catch-up to falls in US stocks in the last two sessions during Japan's market holidays. The Nikkei gained around 9 per cent last year.
US stock futures were up 0.3 per cent, in a knee-jerk reaction to the jump in oil prices, rebounding slightly from a one-week low hit on Dec. 31.
Global oil benchmark Brent futures gained 3.0 per cent to $38.40 per barrel, rising as high as $38.46, its highest since early December.
Saudi Arabia executed a prominent Shi'ite Muslim cleric on Saturday. Riyadh cut ties with Iran after protesters stormed the Saudi embassy in Tehran.
In the currency market, the safe-haven Swiss franc was bid up, gaining 0.4 per cent against the euro to 1.0849 per euro.
The dollar held steady against others for now as investors looked to how much further the US Federal Reserve can raise rates this year after its first rate hike in almost a decade last month.
The euro stood little changed from the end of last year at $1.0851. The dollar fetched 120.31 yen.
An immediate focus will be on business activity surveys on Monday, with concerns about the US and Chinese economies and their policy implications expected to fixate investors again this year.
A private survey at 0145 GMT is expected to show China's factory activity contracted for a 10th straight month in December, while a similar look at US manufacturing is expected to show the sector is still in contraction after having hit a 6-1/2-year low in November.
"It was quite unusual for the Fed to raise rates when the ISM is below 50, (which indicates contraction). And we are likely to see another month of contraction. We have to see how long this will continue," said Masahiro Ichikawa, senior strategist at Sumitomo Mitsui Asset Management.
© Thomson Reuters 2016