Hong Kong's Hang Seng Index rose 1.41 percent by 3:40 p.m. HK/SIN as sharp gains in the materials, property and construction, and financials sectors lifted the index.
Japan's Nikkei 225 advanced 0.51 percent, around 113.49 points, to close at 22,510.48, recovering slightly after the index closed down by more than 300 points on Monday. The iron and steel sector led the climb on Tuesday, rising 2.39 percent, as most sectors recorded gains, with automakers also strengthening as the recent rise in the yen faded.
Over in South Korea, the Kospi reversed earlier declines, closing higher by 0.48 percent to 2,280.20 as markets examined recent corporate results. Steelmaker Posco rose 2.52 percent despite missing earnings estimates on Monday while shipbuilders tumbled. Samsung Heavy Industries fell 2.38 percent and Hyundai Heavy Industries dropped 1.31 percent after both reported operating losses.
Down Under, the S&P/ASX 200 tacked on 0.61 percent to end at 6,265.80 as its materials subindex led gains for the day.
MSCI's Asia Pacific ex Japan index was up 0.62 percent during Asia afternoon trade.
Gains in the region came on the back of a mixed close on Wall Street in the overnight session, with technology shares stateside advancing to a record high in the lead up to major tech names reporting results for the quarter.
Google parent Alphabet jumped after the company reported expectations-topping second-quarter earnings and revenue on Monday. Facebook and Amazon are expected to report corporate results on Wednesday and Thursday, respectively.
More than 17 percent of S&P 500 companies have reported earnings for the previous quarter as of Monday, with 82 percent of those topping expectations, according to FactSet.
Also of note was Monday's rise in U.S. Treasury yields, which tracked volatility seen in the Japanese government bond market overnight. The yield on the 10-year U.S. Treasury note last stood at 2.96 percent after the yield on the 10-year Japanese note climbed to its highest level since February on Monday.
"The 10 (basis point) steepening in the Japanese yield curve is massive in the context of a market that rarely moves more than 1 (basis point)," ANZ analysts said in an early morning note.
The moves came after Reuters reported last week, citing sources, that the Bank of Japan is holding preliminary discussions on potentially adjusting its policy, with a focus on ways to make its stimulus program more sustainable.
"Market moves are likely being exacerbated by low liquidity due to the holiday period, but they reflect a broader fear that central banks are reducing their purchases while U.S. bond supply is set to rise significantly. President Trump has made no secret of his dislike of the Fed’s tightening, which has helped steepen the curve," the ANZ analysts added.
Trump had said in a recent CNBC interview that he was "not thrilled" about the Federal Reserve raising interest rates as that would obstruct economic recovery.
Ahead, meetings by the Bank of Japan and the Federal Reserve next week are expected to be closely watched by markets for more clues on policy.
In currencies, the dollar retraced some of its recent losses amid the move higher in U.S. Treasury yields. The dollar index, which tracks the U.S. currency against a basket of peers, firmed to trade at 94.717. Against the yen, the dollar traded at 111.18 at 3:37 p.m. HK/SIN, but remained above levels around the 110 handle seen during Asia's Monday trade.
In individual movers, shares of Changsheng Biotechnology plunged 9.96 percent, with Tuesday's declines coming on the back of six consecutive sessions of falls. The company is currently embroiled in a vaccine standards scandal in China.