Greater China markets traded higher on the day. The Hang Seng Index reversed early losses to inch higher by 0.16 percent at 3:15 p.m. HK/SIN, eyeing a tenth straight day of increases. The benchmark saw gains of 2.6 percent last week. Most property developers rose, extending gains recorded in the previous session. China Evergrande was higher by 2.79 percent and China Vanke tacked on 2.72 percent at 3:18 p.m. HK/SIN.
On the mainland, the Shanghai Composite climbed 0.54 percent to close at 3,410 and the Shenzhen Composite edged up 0.22 percent to finish the session at 1,945.98. Property plays on the CSI 300, an index of blue chip names listed in Shanghai and Shenzhen, rose 3.33 percent on the day.
MSCI's broad index of shares in Asia Pacific excluding Japan was higher by 0.33 percent at 3:18 p.m. HK/SIN. The index was just under its all-time high of 591.50 set more than a decade ago.
The first trading week of the year had seen Asian markets touch multi-year highs. Hong Kong's Hang Seng Index hit its highest levels in a decade and Japan's benchmark Nikkei 225 rose to levels not seen in 26 years in the last trading day.
Earnings releases from several Japanese corporates are expected toward the end of the week, although Samsung Electronics is set to release its fourth-quarter earnings guidance on Tuesday.
Japanese markets were closed for Coming of Age Day.
U.S. markets closed higher on Friday despite jobs data for the month of December coming in below expectations.
Just 148,000 jobs were added in the U.S. last month, according to government data, compared to the 190,000 increase projected in a Reuters poll. Average hourly earnings were higher by 2.5 percent on an annualized basis.
Still, major indexes stateside recorded gains in the last session to cap off a strong start to the year, with the Dow Jones industrial average climbing 2.3 percent last week.
On the currency front, the greenback remained on the back foot against a basket of currencies, but traded a tad firmer at 92.129 at 3:10 p.m. HK/SIN. That was slightly above Friday's close of 92.013.
"On balance, the U.S. nonfarm payroll numbers ... left the dollar (and Fed rate hike odds) none the worse for wear, but investors we think will continue to channel their attention to the other major global central banks instead," said Emmanuel Ng, an analyst at OCBC Bank.
Against the yen, the dollar firmed to trade at 113.24.
The Australian dollar edged down but continued to trade at the $0.78 handle. The Aussie dollar last traded at $0.7841.
Meanwhile, oil was slightly firmer after slipping in the previous trading session on the back of higher U.S. production. Oil prices had soared to their highest levels since May 2015 earlier last week.
U.S. West Texas Intermediate tacked on 0.28 percent to trade at $61.61 a barrel and Brent crude futures added 0.22 percent to trade at $67.77.
In corporate news, shares of Shenzhen-listed FAW Car closed up 1.49 percent. The automaker announced Sunday that it had agreed to take a 10 percent stake in Mobike Chuxing Technology, the car-sharing arm of mainland bike-sharing start-up Mobike, Reuters reported.
Other mainland-listed automakers were also higher, with Great Wall Motor rising 3.22 percent by the end of the day.