MSCI's broadest index of Asia-Pacific shares outside Japan fell 0.5%, turning negative after the China services purchasing managers' index (PMI) compiled by HSBC/Markit fell to 50.0 in July from a 15-month high of 53.1 in June.
It was the lowest reading since November 2005 when the data collection began, indicating a recovery in the broader economy is still fragile and may need further government support.
"The weakness in the headline number likely reflects the impact of the ongoing property slowdown in many cities as property related activity, such as agencies and residential services, see less business," said HSBC's China Chief economist Qu Hongbin.
Tokyo's Nikkei fell 0.2% and mainland Chinese shares slipped 0.5% from a seven-month high hit just before the data.
US stocks rallied on Monday, lifted by Portugal's decision to rescue Banco Espirito Santo and earnings from Warren Buffett's Berkshire Hathaway.
Currency markets in Asia were focused on the Reserve Bank of Australia's (RBA) policy decision later in the day.
With the RBA widely expected to keep its cash rate unchanged at 2.5%, where it has been for the past year, investors will be looking to the central bank's take on economic conditions and the Australian dollar's perceived strength. The currency has gained about 4.7% versus the dollar so far this year.
"If the RBA maintains a cautious tone, it could renew the decline in AUD but if the statement sounds more balanced the currency will extend its relief rally," Kathy Lien, managing director for BK Asset Management, said in a note to clients.
The Australian dollar edged down to $0.9320, having bounced sharply on Monday from a two-month low of $0.9275 touched last week after a surprisingly large increase in Australian retail sales.
The US dollar was little changed at 102.575 yen, well below the four-month peak of 103.15 hit last week.
The greenback was capped by a fall in Treasury yields overnight after weaker-than-expected US non-farm payrolls data on Friday knocked it off the 103 threshold.
Treasury yields fell as the bond market retained its bullish tone after rallying Friday on the jobs report.
The euro was also effectively flat, at $1.3421 after being hoisted from eight-month lows below $1.34 in wake of Friday's US jobs data release.
The euro has made little further headway since Friday's bounce, weighed by caution ahead of a European Central Bank meeting on Thursday.
In commodities, US crude extended gains from Monday when it rose as market attention shifted from swelling supplies to concerns about ongoing violence in Libya and other global hot spots.
US crude gained 0.1% to $98.41 a barrel.