That decline followed a more than 3% drop on Wednesday after Australia's anti money-laundering and terrorism financing regulator filed for civil penalty orders against the firm, alleging its "oversight of the banking and designated services provided through its corresponding banking relationships was deficient.".

Hong Kong's Hang Seng index declined about 1.5%, as of its final hour of trading, with shares of Chinese tech behemoth Tencent falling 1.85%.

Mainland Chinese stocks declined also ended their trading day lower, with the Shanghai composite down 0.25% to around 2,903.64 and the Shenzhen component shedding 0.35% to 9,774.44. The Shenzhen composite also slipped 0.24% to approximately 1,631.24.

Japan's Nikkei 225 slipped 0.48% to close at 23,038.58, with shares of Tokyo Electron falling 3.44%. The Topix index was 0.1% lower to end its trading day at 1,689.38. In South Korea, the Kospi shed 1.35% to close at 2,096.60 as shares of industry heavyweight Samsung Electronics and SK Hynix fell 1.92% and 2.18%, respectively.

Asia stocks declined on Thursday following a report that an anticipated "phase one" trade deal between the U.S. and China may not be inked by the end of 2019.

Reuters reported, citing trade experts and people close to U.S. President Donald Trump's administration, the completion of a partial trade deal could be pushed into 2020 as China seeks more extensive tariff rollbacks. That report came after The Wall Street Journal reported, citing former Trump administration officials, that the ongoing trade talks could hit an impasse.

For its part, a spokesman for the Chinese commerce ministry told reporters on Thursday that Beijing will strive to reach a "phase one" trade deal with Washington, according to Reuters.

The developments come as Dec. 15 looms, when more tariffs on Chinese goods to the U.S. are set to kick in.

The matter was further complicated by U.S. Congress passing a Hong Kong rights bill, amid ongoing turmoil in the city that has been plagued by civil unrest for months. Chinese Foreign Ministry spokesman Geng Shuang said Beijing "condemns and firmly opposes" the first bill, known as the Hong Kong Human Rights and Democracy Act.

One strategist told CNBC on Thursday that the situation "feels a bit alarming."

"These tensions increase just when it seemed ... there may finally be a deal," Anthony Raza, head of multi-asset strategy at UOB Asset Management, told CNBC's "Squawk Box" on Thursday. He described the situation as "frustrating."

"We can try to do all our assessment on economic projections and model things out but in the end, this feels like a bit of a wildcard," he said. "We don't quite know how … these negotiations will go. We don't quite know how Trump's gonna react to certain requests. And therefore … as an investor … that's a level of uncertainty … that doesn't feel very comfortable."

"I think eventually we'll see a trade deal, but whether we will see one before the end of this year remains to be seen," Vasu Menon, executive director of investment strategy at Singapore's OCBC Bank., told CNBC's "Capital Connection" on Thursday.

"It may spook markets short term, cause a pullback, but I think markets are still hopeful that some form of a phase one — perhaps watered-down — deal will be still seen down the road," Menon said.