Chinese markets traded higher after stronger-than-expected twin PMI surveys gave investors a boost of confidence.
The finished up 0.69 percent, or 21.54 points, at 3,122.03, after China's manufacturing PMI surveys were released, while the Shenzhen composite ended 1.114 percent higher, or 22.836 points, at 2,073.113.
China's official manufacturing purchasing managers' index (PMI) and the private Caixin manufacturing PMI, were out on Tuesday morning. Both surveys showed strong results, with the official survey snapping two months of flat readings with a forecast-beating 51.2 reading for October. The private Caixin survey also hit 51.2, showing the fastest rate of improvement since March 2011.
Australia's benchmark ASX 200 closed down 0.51 percent, or 27.232 points, at 5,290.5, weighed by a 0.52 percent drop in the energy subindex and a 0.54 percent decline in the financials subindex.
The Reserve Bank of Australia announced it would leave cash rates unchanged at 1.5 percent, as labor market indicators remained mixed and inflation pressures were subdued, the central bank's official statement said.
Australian investors are also likely distracted by the upcoming Melbourne Cup, the horse race billed as "the race that stops a nation."
In Hong Kong, the index was up 1.27 percent mid-afternoon, but one debut stock bucked the overall higher trend.
Chinese state-backed Cofco Meat tumbled as much as 24 percent in the first half hour of its first trading day before recovering some losses. Shares of the meat supplier opened at HK$2, but traded at HK$1.68 as of 2:28 pm HK/SIN, down 16 percent.
Japan's finished up 0.1 percent, or 17.38 points, at 17,442.4, after the Bank of Japan stood pat on monetary policy.
The Japanese central bank held rates at -0.1 percent and the pace of bond purchases unchanged, but cut its core consumer inflation forecast for the year ending March 2018 to 1.5 percent from 1.7 percent.
Across the Korean Strait, the Kospi closed down 0.04 percent, or 0.8 points, at 2,007.39, as a political crisis involving President Park Geun-hye weighed on investor sentiment.
Prosecutors launched an investigation after allegations that Choi Soon-sil, a friend of President Park's, had influenced state affairs, gained access to classified material and even benefited through non-profit foundations, Yonhap reported.
"It is important to recognize that South Korea already had economic challenges going into the latest political episode," said Frederic Neumann, co-head of Asian economics research at HSBC. These challenges included the restructuring of its shipping industry, potential tightening of the real estate market, and weak exports, he said.
"The latest political development just makes it harder for the government to respond in a timely fashion to the (structural challenges and) the pressure could head back to the central bank to help sustain growth in the medium term," Neumann added.
The won weakened against the dollar, fetching 1,141 won as of 1:22 pm HK/SIN, above levels as low as 1,129 last week.
The , which tracks the greenback against a basket of currencies, stood at 98.417, as of 2:30 pm HK/SIN.
On the corporate news front, Honda Motor shares dropped 2.04 percent. On Monday, the car maker reported a 38 percent on-year increase in second-quarter operating profit and raised its full-year net profit guidance by 6 percent to 415 billion yen ($3.95 billion), citing strong Chinese demand.
"Investor views remain split on how much Honda is capable of recovering its profitability. Yet we think this was a solid result, a first step towards normalization of the Takata problem and the start of normalization in sales in various regions," Takaki Nakanishi, equity analyst at Jefferies, said in a Monday note.
Panasonic stock was also under pressure, plunging 6.47 percent to 1,026 yen ($9.80) after it was initially untraded amid heavy sell orders.
The Japanese electronics maker cut its full-year sales and profit forecasts on Monday, after it brought forward an investment in a Tesla Motors battery plant. Profit forecasts were slashed by nearly 21 percent for the fiscal year ending March 31 to 245 billion yen ($2.33 billion).
Shares of Sony shed 0.71 percent on losses related to the sale of its battery business, amid a restructuring bid to focus on its core businesses such as gaming and entertainment.
In Australia, Navarre Minerals was up 4.76 percent, giving back some gains after rising as much as 11.9 percent, its highest in over a year and a half. The metal explorer announced it had received commitments from investors to raise A$747,000 ($568,420) through 19.7 million fully paid ordinary shares at an issue price of 3.8 cents a share.
On Monday, OPEC approved a document outlining its long-term strategy, signaling members were making progress on determining how to manage output levels. But oil futures fell as much as 3 percent during Monday's U.S. session, with traders unconvinced OPEC was moving toward an output freeze designed to reduce the global oil glut.
Crude prices recovered in Asian trade, Brent futures were up 0.74 percent, at $48.97 a barrel after settling at $48.30 a barrel, while U.S. West Texas Intermediate (WTI) futures were up 0.6 percent, at $47:14. It last settled in the U.S. at $46.86.
U.S. markets finished near breakeven on Monday. The closed down 0.1 percent at 18,142.42, the S&P 500 and the composite were near unchanged at 2,126.15 and 5,189.13 respectively.
The Philippines' market is closed for a public holiday on Tuesday.