Japan's Nikkei and Chinese bluechips were mostly unchanged, Hong Kong's Hang Seng index eased 0.2% and South Korea gained 0.5%
Private companies in the US added 132,000 jobs in August, indicating a slower growth in a tight labour market, a payroll data company said in a report
Data for June was revised higher to show 398,000 jobs created instead of the previously reported 372,000.
The MSCI All Country stock index was flat at 744.71 points, also down 2% from a record high on Tuesday
The dollar rose to a 2-1/2-month peak on Wednesday, posting its biggest monthly rise since November 2016, supported by a surprisingly hawkish shift in the US Federal Reserve's rate outlook
Private payrolls increased by 978,000 jobs last month, the ADP National Employment Report showed on Thursday
Private payrolls increased by 117,000 jobs last month, the ADP National Employment Report showed on Wednesday
The labour dept said that nonfarm payrolls increased by 209,000 jobs last month amid broad gains
The solid gains in employment likely reflect rising confidence in the economy.