"Amid quiet markets, it is worth pondering the potential impact of the Fed's signaled paring back of its balance sheet. We think there is some logic to the argument that the asset classes that benefited the most from quantitative easing are likely to be among those that might suffer most as it is unwound," ANZ Research said in its Tuesday morning note.
Given the data-light trading session on Tuesday, markets were expected to look ahead to cues from central bankers later in the week, with Fed Chair Janet Yellen due to testify before Congress on July 12 U.S. time.
In individual stocks, Taiwan-listed companies making up part of Tesla's supply chain were mixed after shares of the automaker climbed during U.S. trade. Bizlink and fastener supplier QST rose 2.24 percent and 0.48 percent respectively, but Hota Industrial slid 1.46 percent.
Shares of Japanese automaker Suzuki closed down 1.77 percent after Reuters headlines that Dutch prosecutors were looking into a possible misuse of emissions software.
Meanwhile, shares of Japan Post Holdings closed up 1.85 percent following a Nikkei report that the Japanese finance ministry would not sell shares of the company as initially planned.
Major gaming stocks listed in Hong Kong traded in the money. Wynn Macau was up 0.68 percent, Sands China rose 0.73 percent and Galaxy Entertainment was up 0.54 percent.
Daily gross gaming revenues (GGR) averages at Macau casinos were up 76 percent last week, compared with estimates for the prior week, Nomura research analysts said in a Monday note. This was partially due to stronger visitation from Hong Kong after President Xi Jinping's visit earlier in the month. Still, monthly GGR growth is expected to decelerate going into the second half of the year, the analysts added.
In Malaysia, Lotte Chemical Titan Holding slipped to trade at 6.33 Malaysian ringgit after opening flat at 6.50 ringgit on its first day of trading, Reuters said. The company was delisted from the Malaysia Stock Exchange in 2011 after Lotte Chemical acquired a controlling stake in it.
Shares of Singapore-listed commodity trader Noble Group traded up 5.6 percent after Goldilocks Investment Company — a fund launched by Abu Dhabi Financial Investment — raised its stake in Noble from 5.03 percent to 8.19 percent, a Singapore Exchange filing showed on Monday.
In energy news, oil prices made slight gains in the last session although concerns remained over the oversupply in markets. U.S. West Texas Intermediate crude rose 0.61 percent to trade at $44.67 a barrel and Brent crude gained 0.55 percent to trade at $47.14 a barrel.
In currencies, the dollar index, which measures the dollar against a basket of currencies, firmed to trade at 96.153.
The Australian dollar edged up following the rise in iron ore prices overnight to above $60 a ton. The Aussie dollar traded at $0.7623 at 2:40 p.m. HK/SIN.
"The Aussie dollar is another market on hold, setting up a short-term trading range between $0.7635 and $0.7570 against the dollar," Ric Spooner, chief market analyst at CMC Markets, said in a note.
While iron ore prices trading above $60 a ton was supportive for the Aussie, its spot price stalling since hitting a peak of $64.95 on June 30 has contributed to the Aussie being on hold, Spooner added.
Major indexes closed mostly higher on Wall Street as markets got set for earnings season. Technology stocks posted gains, with Amazon shares rising 1.8 percent as the company rolled out its annual Prime Day shopping event.