In the Greater China region, the Shanghai composite declined about 1.18 percent to close at around 2,579.70 and the Shenzhen component fell 1.435 percent to finish its trading day at approximately 7,516.79. The Shenzhen composite also shed 1.171 percent to close at about 1,314.58.
Hong Kong's Hang Seng index slipped almost 1 percent, as of its final hour of trading.
Beijing announced on Monday that the Chinese economy grew 6.6 percent in 2018, which was the slowest pace since 1990. Meanwhile, the official Xinhua News Agency reported that Chinese President Xi Jinping said the country needed to be on guard for "black swan" events while also preventing "grey rhino" events.
A black swan event is an unforeseen occurrence that has dire consequences whereas a grey rhino is an obvious threat that is ignored.
"The grey rhino is very clear, it's the high level of debt in the whole economy from the government, the local government, and to the privately-owned enterprises and also the state-owned enterprises, this is one thing that nobody can overlook," Francis Lun, CEO of Geo Securities, told CNBC's "Street Signs" on Tuesday.
"For the black swan event, last year we had the U.S.-China trade war and this year we don't know ... what could happen but maybe ... the black swan can turn into a white swan and then we'll reach some kind of agreement with the U.S. and ease the trade tensions," Lun said.
Officials from the U.S. and China are attempting to reach a deal to ease trade tensions between the two economic powerhouses, which rocked global markets for much of 2018.
In Japan, the Nikkei 225 fell 0.47 percent to close at 20,622.91 while the Topix index declined 0.63 percent to finish its trading day at 1,556.43. Shares of index heavyweight Fast Retailing, the company behind the Uniqlo chain of apparel stores, slipped 0.51 percent.
Australia's ASX 200 declined by 0.54 percent to close at 5,858.8, with the sectors mixed. The heavily-weighted financial subindex Down Under declined 1.18 percent as shares of the country's so-called Big Four banks saw losses. Australia and New Zealand Banking Group slipped 1.45 percent, Commonwealth Bank of Australia declined 1.19 percent, Westpac fell 1.72 percent and National Australia Bank shed 1.28 percent.
Futures also pointed to a lower open for U.S. stocks on Tuesday. Dow Jones Industrial Average futures implied an opening decline of 178.35 points for the index, as of 2:01 a.m. ET Tuesday. S&P 500 and Nasdaq futures also pointed to losses.