Data last week showed China's manufacturing activity sped up in September, with the official Purchasing Managers' Index rising to 51.1 from 51.0 in August and just below analyst forecasts. It followed the HSBC PMI survey, which showed factory activity expanded at a slower-than-expected pace last month.
(Read more: China September HSBC PMI well below flash estimate)
"The China trade data will be closely watched – the PMI data has been encouraging although the private, survey of smaller firms has not been that strong," said Desmond Chua, a market analyst at CMC Markets, referring to the HSBC survey.
"Hopefully we will get some good data out of China and that will be a silver lining for the market after the U.S. budget woes," he added.
Gridlock in Washington over budget negotiations and a government shutdown that led to the postponement on Friday of the key U.S. non-farm payrolls report, undermined sentiment in global markets last week.
Developments in Washington on the budget and a looming debt ceiling were expected to remain a key focus this week.
"We have seen tepid trade in Asia because we have no idea how events in the U.S. will play out," said Stan Shamu, market strategist at trading firm IG. "The impact of the government shutdown so far has not been too significant but it is something to watch."
On the calendar
Elsewhere, investors will be watching the September jobs numbers from Australia on Thursday, industrial production data from India on Friday, while third quarter economic growth numbers from Singapore could also be released this week.
(Read more: Why Singapore's economy looks set for a contraction)
Unusually strong annualized quarter-on-quarter economic growth in the second quarter and recent weak data from Singapore means many economists anticipate a contraction in the third quarter, when measured on a quarterly basis.
Singapore's central bank meanwhile is expected to meet either this week or early next week, with analysts expecting no major change in monetary policy.
Elsewhere, South Korea's central bank meets on Thursday and Bank Indonesia holds a meeting on Tuesday.
"We expect Bank of Korea to keep monetary policy on hold, reflecting the central bank's forecast of a gradual recovery in growth and inflation and Bank Indonesia will likely stay on hold at 7.25 percent given the recent low inflation reading," analysts at Bank of America Merrill Lynch said in a note.
Indonesia's annual inflation rate stood at 8.4 percent in September, easing from 8.79 percent in August.
—By CNBC.Com's Dhara Ranasinghe; Follow her on Twitter @DharaCNBC