Trading this week is likely to turn on data from China and the U.S. and the ECB meeting. Last week, Asian stock markets were buffeted by weak U.S. consumer spending and sluggish growth in Chinese industrial profits.
A preliminary reading of China's manufacturing activity in June, due Tuesday, will be scrutinized for evidence the slowdown in the world's No. 2 economy has stabilized.
Monthly U.S. employment figures are due Thursday. On the same day, the European Central Bank holds its monthly rate-setting meeting, where it is widely expected to keep its policies unchanged, having taken aggressive steps last month to help the economy.
In Asia, most markets closed higher. Japan's benchmark Nikkei 225 gained 0.4 percent to 15,162.10, reversing morning losses. Japan's economy ministry said the country's industrial output recovered slightly in May from a fall in the previous month.
South Korea's Kospi was up 0.7 percent to 2,002.21 and China's Shanghai Composite Index advanced 0.6 percent to 2,048.33.
Stocks in Taiwan, Thailand and Indonesia also rose. But Australia's S&P/ASX 200 fell 0.9 percent to 5,395.70, one day ahead of the central bank's rate-setting meeting.
Hong Kong's Hang Seng shed 0.1 percent to 23,190.72.
In energy trading, benchmark U.S. crude for August delivery was down 17 cents to $105.57 per barrel in electronic trading on the New York Mercantile Exchange. The contract fell 10 cents on Friday.
In currencies, the dollar slipped to 101.38 yen from 101.41 yen late Friday. The euro rose to $1.3664 from $1.3648, reversing an earlier drop.