Meanwhile, Australia's S&P/ASX 200 tacked on 0.21 percent to end at 5,841.30, with gains led by energy and utilities stocks.
Greater China markets underperformed their regional peers. Hong Kong's Hang Seng Index slid 1.75 percent by 3:10 p.m. HK/SIN as financials and technology names took a hit. Property developers were also downbeat, with China Evergrande tumbling 5.3 percent before the market close.
Those declines came as the Hong Kong dollar, which is pegged to the greenback, remained close to the weak end of the currency's trading band.
On the mainland, the Shanghai composite lost 1.53 percent to close at 3,110.75 and the Shenzhen composite eased 0.52 percent to end at 1,824.77. The blue chip CSI 300 index, meanwhile, fell 1.6 percent on weakness in insurers and banking names.
MSCI's broad index of shares in Asia Pacific excluding Japan was down 0.69 percent at 3:03 p.m. HK/SIN.
Despite that, U.S. stock index futures were trading higher during Asia hours, but had pared some of the steeper gains seen earlier in the day. As of 12:04 p.m. HK/SIN, the implied open for Dow futures was up around 83 points. S&P 500 and Nasdaq futures were also in the green.
Still, markets were calm, for the most part, following U.S.-led precision missile strikes in Syria on Friday U.S. time. The strikes, carried out in conjunction with the U.K. and France, were intended to serve as a deterrent against chemical weapons.
The airstrikes on Friday "have thus far drawn only verbal condemnation from Russia ... with Russia's prediction of 'global chaos' if the West hits Syria again not filling markets with fresh dread, at least judging from the limited foreign exchange market movements evident in the first two hours of the new trading week," Ray Attrill, head of foreign exchange strategy at National Australia Bank, said in a morning note.
Against the yen, the dollar edged down slightly to trade at 107.21 at 3:01 p.m. HK/SIN after touching as high as 107.61 earlier in the session.
Tensions related to a trade spat between the U.S. and China, the world's two largest economies, appeared to fade after dominating headlines in recent weeks.
"[T]here is some evidence that both sides have somewhat backed down slightly after [Chinese President] Xi [Jinping] championed free trade at Boao Forum and Trump expressed optimism that a trade deal might eventually be agreed," Zhu Huani, an economist at Mizuho Bank, said in a note.
Still, trade-related issues were unlikely to be far from investors' minds after a report from The Wall Street Journal last week that Trump was threatening to block Chinese tech investment in the U.S.
Stocks stateside had declined on Friday, weighed down by bank earnings. Results released last week by Citigroup, Wells Fargo and J.P. Morgan Chase surpassed analyst expectations, and traded higher before falling as markets had already priced in the strong results.
On the commodities front, both U.S. West Texas Intermediate and Brent crude declined after recording their best week since July on Friday.
U.S. crude futures lost 1.23 percent to trade at $66.56 per barrel after rising more than 8 percent last week. Brent crude futures were lower by 1.35 percent at $71.60.
The dollar index, which tracks the U.S. currency against six major peers, stood at 89.747.
In individual movers, Hong Kong-listed shares of Russian aluminum company Rusal tumbled 28.92 percent by 3:01 p.m. HK/SIN following news that the U.S. was preparing additional sanctions against Russia. U.S. Ambassador to the United Nations Nikki Haley said Sunday that those measures would be announced on Monday U.S. hours, Reuters reported.