Tokyo shed 0.37%, or 57.69 points, to finish at 15,379.44 and Sydney dipped 0.11%, or 6.1 points, to close at 5,518.9. Seoul lost 0.23%, or 4.54 points, to 2,005.12.
Shanghai was flat, edging up 0.55 points to 2,059.93. Hong Kong also ended flat, edging down 5.44 points to 23,540.92.
With Wall Street closed on Friday for the Independence Day holiday, there were few catalysts to drive regional markets after they ended last week mixed.
The Labor Department said on Thursday that the US economy added 288,000 jobs last month — well above expectations of 215,000, adding to the sense that a recovery is well on track. The unemployment rate fell to 6.1% from 6.3% in May.
Focus is now on Beijing, where the government will on Wednesday release inflation data, followed Thursday by trade statistics.
On currency markets, the dollar maintained its recent gains against the yen that were boosted by the US jobs report.
The greenback bought 102.10 yen in afternoon Tokyo trade, compared with 102.08 yen on Friday.
The euro was at $1.3593 and 138.67 yen against $1.3600 and 138.90 yen.
Oil prices were mixed. US benchmark West Texas Intermediate for August delivery eased 12 cents to $103.94 while Brent crude rose nine cents to $110.73.
Gold fetched $1,314.03 an ounce at 1120 GMT compared with $1,322.84 late Friday.
Jakarta ended up 1.70%, or 83.21 points, to close at 4,989.03. Bank Negara Indonesia climbed 2% to 4,845 rupiah, while Indah Kiat Pulp & Paper lost 0.74% at 1,350 rupiah.
Kuala Lumpur gained 0.40%, or 7.59 points, to close at 1,892.50. SapuraKencana Petroleum rose 0.7% to 4.40 ringgit, while Telekom Malaysia added 0.8% to 6.37. Axiata Group lost 0.4% to 6.89 ringgit.
Manila rose 0.53%, or 36.82 points, to 6,999.10.
Mumbai rose 0.53% to end at 26,100.08 points. It had touched a new high of 26,123.55 points during the session.
IDFC rose 6.23% to 142.30 rupees, while Container Corp gained 6.20% to 1,348.05 rupees.
Singapore rose 0.59%, or 19.32 points, to 3,291.57. Vehicle distributor Jardine Cycle & Carriage rose 2.34% to S$45.52 while oil rig-maker Keppel Corp gained 0.46% to S$10.82.
Taipei edged up 0.11%, or 10.15 points, to 9,520.2. Taiwan Semiconductor Manufacturing Co was 0.74% higher at T$136.0, while Formosa Plastics closed down 0.65% at T$77.0.
Wellington was flat, edging down 2.55 points to 5,186.36. Telecom fell 0.93% to NZ$2,67 and Trade Me rose 1.67% to NZ$3.65.