- Wall Street had a volatile session overnight which saw the Dow recover from a 507-point drop.
- Meanwhile, U.K. Prime Minister Theresa May delayed a Brexit vote that was set to take place on Tuesday in the U.K. parliament. The pound plunged to 21-month lows on the back of that announcement.
- Also on Monday, the Reserve Bank of India's chief, Urjit Patel, resigned abruptly, stoking concerns over the independence of the central bank.
Stocks in Asia traded mixed on Tuesday afternoon on the back of a volatile session on Wall Street which saw the Dow recover from a 507-point drop.
The mainland Chinese markets saw gains by the end of their trading day. The Shanghai composite rose 0.37 percent to close at around 2,594.09 while the Shenzhen composite advanced 0.853 percent to finish the trading day at about 1,343.90.
Hong Kong's Hang Seng index also recovered to close slightly higher at 25,771.67, or about 0.07 percent.
Meanwhile in Japan, the Nikkei 225 fell 0.34 percent to close at 21,148.02 percent while the Topix index declined by 0.91 percent to close at 1,575.31.
Shares of Japanese conglomerate Softbank gained 2.45 percent after the company announced on Monday that shares of its mobile unit IPO would be priced at 1,500 yen apiece (approx. $13.25). Softbank is expected to raise 2.65 trillion yen from the listing (approx. $23.4 billion).
Samsung Biologics surged 17.79 percent on the day after South Korea's stock exchange decided on Monday to allow it to continue trading following a suspension in mid-November over concerns it had intentionally breached accounting rules ahead of its listing in 2016.
Australia's gained 0.42 percent to close at 5,575.90, with most sectors seeing gains.
Shares of Australia's so-called Big Four banks saw gains on the day. Australia and New Zealand Banking Group rose 0.53 percent and Commonwealth Bank of Australia advanced by 0.23 percent, Westpac rose 0.80 percent and National Australia Bank climbed up by 0.43 percent.
The move was confirmed in a statement by May to lawmakers in the House of Commons on Monday afternoon.
The now-delayed vote in the House of Commons, termed the "meaningful vote," was to allow lawmakers to accept or reject the terms of Brexit that the EU and British government had previously agreed.
May claimed that while there was broad support for her deal, the issue of the Northern Irish backstop remained a concern and she would return to European counterparts to renegotiate the deal.
"I will hold emergency talks with EU leaders to discuss possible changes to backstop," May said.
One analyst, however, told CNBC's "Squawk Box" on Tuesday that the uncertainty surrounding Brexit could actually present buying opportunities for Asian companies.
"I think increasingly, looking at the U.K., not only is the stock market weak, but the currency is weak as well," said Jim McCafferty, head of Asia (ex-Japan) research at Nomura Securities.
"From an outside investor's point of view, the assets are getting cheaper in local currency terms and assets are getting cheaper in stock market terms," McCafferty added. "So that might be an opportunity for acquisitive Asian companies to buy strategic assets in the U.K."
In overnight market action stateside, the Dow Jones Industrial Average erased an intraday 507-point drop to close 34.31 points higher at 24,423.26 while the advanced 0.2 percent to finish the trading day at 2,637.72. The Nasdaq Composite rose 0.7 percent to close at 7,020.52.
At its lows of the day, the S&P 500 dipped below its low reached in October during the previous major market sell-off. These technical breakdowns typically lead to more selling as some computer programs are set to dump stocks on those levels.
The Reserve Bank of India's governor, Urjit Patel, resigned with immediate effect on Monday, raising concerns over the independence of the central bank.
The primary focus for investors is whether Patel resigned due to growing pressure from India's government to lower rates and conduct looser monetary policy as the countdown to next year's general election kicks off. Patel was reportedly criticized by the government for the central bank's relentless push to clean up India's banking sector.
Patel's resignation comes less than three years after his predecessor Raghuram Rajan was not confirmed for a second term as central bank governor in 2016, possibly due to growing tensions between him and India's government.
Following the announcement, the rupee fell sharply against the dollar. The Indian currency was last at 71.794 against the greenback, after seeing an earlier low of 72.49.
"Urjit Patel's resignation for 'personal reasons', well before the expiry of his term in September 2019, in fact, goes to reinforce the widened rift between the central bank and the government," Prakash Sakpal, an economist at ING, said in an article published on Monday.
"Clearly, central bank independence is compromised, and the government indeed now has greater control of the central bank and its reserves, which are required to plug the widening fiscal deficit in the election year," Sakpal said.
The U.S. dollar index, which tracks the greenback against a basket of its peers, was at 97.060 after rising from levels around 96.4 yesterday.
— Reuters and CNBC's Fred Imbert, David Reid and Seema Mody contributed to this report.