Down Under, the S&P/ASX 200 shed 0.51 percent. Major sectors were down, including financials, oil producers, and mining companies.
Greater China markets edged higher, with Hong Kong's Hang Seng Index up by 0.17 percent at 3:40 p.m. HK/SIN as developers and technology stocks moved higher on the whole. However, it was weighed down by declines across the gaming sector. On the mainland, the Shanghai composite rose 0.75 percent.
MSCI's broad index of shares in Asia Pacific excluding Japan was flat for the most part, last trading higher by 0.03 percent.
The lukewarm moves came on the back of gains seen stateside on Monday, with the Nasdaq composite posting a record close — its first since March 12. The index rose 0.69 percent as technology names advanced, with Apple and Amazon notching record closing highs.
Other major stock indexes also recorded gains, with the Dow Jones industrial average rising 0.72 percent, or 178.48 points, to close at 24,813.69. Those gains followed the release of expectation-surpassing U.S. jobs numbers on Friday.
Meanwhile, investors continued to keep an eye on lingering trade concerns after the U.S. imposed tariffs on steel and aluminum imports from the European Union, Canada and Mexico, while coming away with no major breakthroughs from the most recent round of trade talks with China.
That comes in the lead-up to a meeting of world leaders at the G-7 summit in Canada this week.
"Ahead of this, markets will be looking to see multilateral co-operation on economic issues in the light of recent anxieties about trade," ANZ analysts said in a note.
In foreign exchange, the dollar index, which tracks the greenback against a basket of currencies, stood at 94.063. Against the yen, the dollar was at 109.83 at 3:42 p.m. HK/SIN.
On the commodities front, oil prices recovered some losses after sliding in the last session on expectations that OPEC members would increase production. U.S. crude futures were up 0.62 percent at $65.15 per barrel. Brent crude futures were up 0.32 percent at $75.53 after settling 2 percent lower on Monday.
In company news, China has launched an investigation into South Korea's Samsung Electronics and SK Hynix as well as U.S. Micron Technology, Reuters reported. Citing a source, the report said that China was probing price-fixing allegations as DRAM — a form of data storage — prices had risen sharply.
Samsung Electronics shed 0.59 percent and SK Hynix was last higher by 0.56 percent.