Hong Kong's Hang Seng Index climbed 0.41 percent by 3:00 p.m. HK/SIN, with the energy sector leading gains before the market close. Financials were higher for the most part, with HSBC up 0.89 percent at 3:00 p.m. HK/SIN, while technology stocks slid ahead of the close.
Mainland indexes dipped below the flat line but finished higher, extending the sharp gains seen on Monday. The benchmark Shanghai composite rose 0.44 percent to close at 2,827.44. The Nasdaq-style Chinext index rose 0.9 percent while the blue-chip CSI 300 index finished up 0.24 percent.
Down Under, the S&P/ASX 200 turned lower, giving up early gains to close down 0.44 percent at 6,258.10 as the heavily weighted financials subindex dropped 1.01 percent amid declines seen across most sectors.
MSCI's index of shares in Asia Pacific excluding Japan traded higher by 0.07 percent during Asia afternoon trade.
With earnings season ahead, trade tensions appear to have dissipated slightly from the spotlight.
Fears that a months-long trade dispute between the U.S. and a number of its trading partners have kept investors on edge about the implications of a potential trade war on global growth. U.S. tariffs on $34 billion in Chinese goods took effect on Friday, with China immediately retaliating with duties on the same amount of U.S. products.
"No new news from the U.S.-Sino trade war has helped investors focus back on fundamentals and with the U.S. earnings season starting later this week, the U.S. has led the gains in equities overnight," Rodrigo Catril, senior foreign exchange strategist at National Australia Bank, said in a note.
Even with the improvement in risk appetite seen so far this week, trade jitters are expected to continue to simmer in the longer term.
"Trade war risk is likely to linger in the background as countries start to introduce measures to prepare for tariffs staying for a potentially longer-than-expected period," Zhu Huani, an economist at Mizuho Bank, said in a note.
The overall improvement in sentiment also came after Wall Street closed sharply higher in the last session, supported partially by the release of expectation-topping June jobs data on Friday. The Dow Jones Industrial Average rose 1.31 percent, or 320.11 points, to close at 24,776.59, posting its best session in more than one month.
Elsewhere, U.K. Foreign Secretary Boris Johnson has resigned and will be replaced by Jeremy Hunt. That development came after Brexit Secretary David Davis stepped down on Sunday as he had objected to British Prime Minister Theresa May's EU withdrawal plan.
The British pound remained under pressure amid the political turmoil. The currency traded at $1.3246 at 2:44 p.m. HK/SIN after taking a hit overnight on the resignation news.
The dollar index, which tracks the greenback against a basket of currencies, firmed to trade at 94.203. Against the yen, the dollar firmed to trade above the 111 level, and was last at 111.08.
In individual movers, Yahoo Japan popped 11.39 percent after SoftBank Group said its subsidiary will buy shares worth around 221 billion yen ($1.99 billion), or a 10.78 percent stake, in Yahoo Japan. Those shares are currently held by Altaba.
Meanwhile, Nissan Motor said Monday it had discovered misconduct in exhaust emissions and fuel economy measurement tests. Shares of the automaker were up 3.79 percent, moving in the same direction as other major Japanese automakers.
Shares of oil refiners Idemitsu Kosan and Showa Shell Sekiyu finished up 12.6 percent and 9.65 percent, respectively, after the companies came to a consensus on a merger next year.
And on the economic front, China's June consumer price index rose 1.9 percent compared to one year ago, in line with analyst forecasts in a Reuters poll. The producer price index, meanwhile, rose 4.7 percent from one year ago, topping the 4.5 percent expected.