Meanwhile, Hong Kong's Hang Seng Index shed 0.17 percent by 3:02 p.m. HK/SIN, with property and materials stocks slumping before the market close, although some of those losses were offset by gains in the utilities sector.
South Korean stocks closed lower, with the Kospi slipping 0.39 percent to 2,301.99. Bank stocks declined, weighing on the broader index, but automakers climbed, with Hyundai Motor closing up 2.86 percent. In Australia, the S&P/ASX 200 edged down by 0.43 percent to 6,241.50, with health care among the worst-performing sectors.
Meanwhile, markets in Japan were closed for a holiday on Monday.
MSCI's index of shares in Asia Pacific excluding Japan slipped 0.41 percent in Asia afternoon trade.
The moves lower came despite gains on Wall Street in the previous session. The S&P 500 added 0.11 percent to end at 2,801.31, closing the session above the 2,800 level for the first time since Feb. 1.
Despite the broader increase stateside on Friday, bank stocks had dipped as markets digested the release of second-quarter earnings. Just over 5 percent of S&P 500 companies have reported second-quarter results so far. Analysts polled by FactSet expect second-quarter earnings to have grown by 20 percent.
Still, the overall gains came amid relief among investors over the lack of fresh, negative trade war headlines, according to analysts, with major U.S. indexes posting strong gains last week. A similar picture was seen in Asia last week, with markets finishing the week higher.
That had come after stocks initially slid following the Trump administration releasing a list of $200 billion in Chinese goods that could be subject to new tariffs, firing the latest shot in the trade dispute between the U.S. and China. The announced duties will only take effect following a review process and come on the heels of U.S. tariffs on $34 billion in Chinese products taking effect earlier in the month.
Despite Monday's slight declines and lingering anxiety on the trade front, some expect regional markets to head higher in the next quarter.
"If you look at particularly the Hong Kong, China market, most of the indicators that I look at are at oversold extreme. They're at a level where I would look for the Hong Kong market ... to try and find a base," Mark Jolley, global strategist at CCB International Securities, told CNBC's "Squawk Box."
He added that unless the trade situation deteriorates significantly, which is seen as unlikely in the short term, Asian markets could see a relief rally in the next one to two months.
Others were more wary in the interim: "In the short term, we prefer to remain cautious on both the A-share and H-share markets, at least until we receive more clarity on a near term resolution to negative drivers," Amundi Asset Management said in a recent research note, adding that the critical risk of a potential trade war still remained.
In currencies, the dollar index, which tracks the U.S. dollar against a basket of currencies, softened to trade at 94.644 at 2:46 p.m. HK/SIN. Against the yen, the dollar traded at 112.36.
Apart from that, investors awaited Federal Reserve Chairman Jerome Powell's semi-annual congressional testimonies on Tuesday and Wednesday during U.S. hours.
In individual movers, telecommunications equipment maker ZTE got a boost after the U.S. removed a ban on the company from purchasing technology from U.S. corporations. Shares of ZTE listed in Hong Kong were up 16.3 percent by 3:08 p.m. HK/SIN while Shenzhen shares closed higher by the daily limit of 10 percent.
Meanwhile, shares of Xiaomi fell 2.56 percent by 3:08 p.m. HK/SIN after media reports that Chinese stock exchanges said the connect scheme linking Hong Kong and the mainland would not extend to firms with weighted voting rights structure. That would mean that shares of Xiaomi will not be accessible to investors on the mainland under the connect program.
— CNBC's Fred Imbert contributed to this report.