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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 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.
The IMF reduced its estimate for global growth on Monday, cautioning that the economic momentum seen in recent years is slowing.
The IMF now projects a 3.5 percent growth rate worldwide for 2019 and 3.6 percent for 2020. These are 0.2 and 0.1 percentage points below its last forecasts in October — making it the second downturn revision in three months.
"A range of triggers beyond escalating trade tensions could spark a further deterioration in risk sentiment with adverse growth implications, especially given high levels of public and private debt," the Fund said.
These potential triggers include a "no-deal" Brexit for the U.K. and a deeper-than-envisaged slowdown in China. The IMF report comes on the back of China reporting its slowest economic growth in almost three decades.
Speaking at the World Economic Forum in Davos, Christine Lagarde, managing director of the IMF, said: "After two years of solid expansion, the world economy is growing more slowly than expected and risks are rising. But even as the economy continues to move ahead ... it is facing significantly higher risks."
The latest cut from the IMF "is just a confirmation of existing concerns of a slower 2019," Singapore's OCBC Treasury Research said in a morning note.
The U.S. dollar index, which tracks the greenback against a basket of its peers, was at 96.430 after touching an earlier low of 96.305.
The Japanese yen, widely viewed as a safe-haven currency, traded at 109.39 against the greenback after seeing an earlier low of 109.69. The Australian dollar was at $0.7129 after slipping from highs of about $0.717 yesterday.
— Reuters and CNBC's Silvia Amaro contributed to this report.