MSCI's broadest index of Asia-Pacific shares outside Japan reversed early losses to rise 0.1 percent.
Chinese shares rose, with the blue-chip index up 0.15 percent and the Shanghai Composite up 0.2 percent. Hong Kong's Hang Seng rose 0.6 percent.
The official Chinese manufacturing and services purchasing managers' indices both slipped in July, but remained above the 50-point mark that separates growth from contraction on a monthly basis.
Investors remained wary after North Korea conducted another missile test late on Friday that it said proved its ability to strike the U.S. mainland. The U.S. responded by flying two bombers over the Korean peninsula on Sunday.
"The geopolitical overhang will likely keep top side moves in check early in the week as the disorganised U.S. and China policy towards North Korea is not helping matters," Stephen Innes, head of Asia-Pacific trading at OANDA, wrote in a note.
The Korean won was up 0.1 percent on Monday at 1,122.2 won to the dollar, after sliding almost 0.7 percent on Friday. South Korea's KOSPI fell 0.3 percent.
Australian shares advanced 0.3 percent.
The perceived safe-haven Japanese yen strengthened, with the dollar shedding 0.2 percent to 110.48 yen, touching its weakest levels since mid-June.
Japan's Nikkei fell 0.1 percent, with the firm yen offsetting news the country's industrial output rebounded in June from a decline in May.
On Wall Street on Friday, the S&P and Nasdaq indexes fell after earnings from companies including Amazon, Exxon Mobil and Starbucks disappointed.
But the Dow closed higher and set an intraday record, lifted by Chevron's strong earnings.
U.S. corporate results overall have come in better than expected for the second quarter. More than halfway through reporting season, S&P 500 companies are on track to have increased earnings by 10.8 percent, according to Thomson Reuters I/B/E/S.
The dollar index, which tracks the greenback against a basket of six major peers, edged up 0.1 percent to 93.376, after Friday's 0.6 percent decline.
Markets are awaiting speeches by Cleveland Federal Reserve President Loretta Mester and San Francisco Fed President John Williams on Tuesday for further insight into whether the central bank has turned more dovish in light of recently muted inflation.
Investors will also be keeping a close eye on data including eurozone core inflation for July on Monday; the Reserve Bank of Australia's rate decision, at which it is expected to stay on hold, and U.S. manufacturing conditions, due Tuesday; the Reserve Bank of India's meeting on Wednesday, at which it is expected to cut rates; and Bank of England on Thursday, where it is likely to leave rates unchanged.
A raft of private manufacturing surveys will also be released on Tuesday.
"It's a huge week on the data front, but for USD bulls there's an unpalatable reality that with (European Central Bank) members sounding increasingly hawkish and their (Fed) counterparts ever so dovish. Anything to confirm this bias will be pounced on by traders," Innes wrote.
The euro was steady at $1.1741, following Friday's 0.6 percent gain.
In commodities, oil prices rose for their sixth straight session on bigger-than-expected inventory drawdowns and signs that Saudi Arabia will reduce output further in August.
U.S. crude futures rose 0.3 percent to $49.85 a barrel, after earlier hitting $50.06, their first foray above $50 in two months.
Brent crude advanced 0.3 percent to $52.69, adding to Friday's 2 percent surge.
Gold rose to $1,1270.98, its highest since June 14 early on Monday and was last steady on the day at $1,26789 an ounce.
© Thomson Reuters 2017
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)