Japanese shares were boosted by a survey which showed corporate sentiment had turned positive for the first time in two years, as optimism about Prime Minister Shinzo Abe's radical stimulus policies offset concerns about recent market volatility.
"The risk is that the economy may be doing well enough that it actually dis-incentivizes the drive for structural reform. That would certainly lead to a dampening of market sentiment," said Alistair Newton, senior political analyst at Nomura.
(Read More: Will the Strong Tankan Send Abenomics Off Course?)
However, data from China showed that industrial activity continued to decline in June, amid concerns about overcapacity and weak demand.
"I think the story for China is basically that there is not any story left. Economic activity has peaked and we think that data will surprise on the downside," said Sailesh Jha, chief strategist at Arcus Capital Singapore.
On the economic front, May construction spending and June ISM survey on manufacturing data are expected to be reported at 10 am ET. Economists surveyed by Reuters expect a gain of 0.6 percent for construction spending and forecast a reading of 50.5 for manufacturing.
"With time running out until the September FOMC [Federal Open Market Committee], such prints are going to be huge for markets," wrote Deutsche Bank's Jim Reid.
(Read More: The Market's Next Worry? The June Jobs Report)
This week will be an extremely light on earnings, ahead of the official start of the second quarter earnings season on July 4. No major companies are expected to report results before the start of trade on Monday.
In Europe, shares traded mixed after data suggested euro zone manufacturing activity stabilized last month, sparking concerns the European Central Bank might move to tighten monetary policy.
In other corporate news, Onyx Pharmaceuticals confirmed it had rejected a purchase offer from Amgen, the world's biggest biotech company.
At the same time, Dow component 3M declined after Morgan Stanley cut the company to "equal weight" on belief that the stellar 22-percent gain over the past year may have run its course.
Online radio provider Pandora jumped following a Morgan Stanley upgrade to "overweight" on belief that the company "pureplay exposure to the secular shift of radio dollars to online channels."