Over in Seoul, the Kospi shed 0.12 percent to close at 2,510.23. Talks between North and South Korea, the first of their kind in more than two years, resulted in North Korea stating it would send a delegation to the upcoming Winter Olympics hosted by the South, Reuters said, citing a South Korean official.
Also of note, South Korea announced Tuesday it would give thought to briefly lifting sanctions against the North if required, in order for the latter to take part in the games.
Shares of Samsung Electronics fell 3.11 percent after the company announced its fourth-quarter earnings guidance on Tuesday. The tech giant said it was estimating a record 15.1 trillion Korean won ($14.13 billion) in operating profit for the quarter. Still, that was a touch below the 15.9 trillion won forecast by Reuters.
Other technology names were mixed. SK Hynix closed down 1.66 percent and LG Electronics climbed 3.81 percent after its stock stumbled in the last session following a lower-than-expected fourth-quarter profit estimate.
Over in Sydney, the S&P/ASX 200 clung to gains, closing 0.09 percent higher at 6,135.8. The resource sector was the best-performer of the day, with major mining companies Rio Tinto and BHP rising 2.34 percent and 1.67 percent, respectively.
Greater China markets were also slightly higher. Hong Kong's Hang Seng Index edged up 0.37 percent at 3:07 p.m. HK/SIN, as investors eyed an 11th straight days of gains. Technology firms and casinos were mostly higher, with Tencent soaring 1.23 percent and Sands China higher by 4.01 percent at 3:09 p.m. HK/SIN.
On the mainland, the Shanghai Composite tacked on 0.16 percent to close at 3,414.83 and the Shenzhen Composite rose 0.32 percent to end at 1,952.18.
U.S. stocks closed mixed on Monday. With no major data released stateside overnight, investors there looked to quarterly earnings releases due at the end of the week.
Several major U.S. banks, including J.P. Morgan and Wells Fargo, are among the first names reporting on Friday and investors will be looking for signs about how changes in the taxcode will impact businesses.
The Dow Jones industrial average edged down 0.05 percent, or 12.87 points, to close at 25,283. Other indexes notched slight gains.