The Nikkei 225 slipped 0.77 percent, or 165.04 points, to close at 21,252.72. The index had pared losses of around 1 percent earlier in the day to hover around the flat line, before sliding once again.
The iron and steel sector, which would likely be affected if recently announced tariffs were implemented by the Trump administration, fell by 2.12 percent.
South Korea's Kospi shed 0.4 percent to close at 2,401.82 after notching gains earlier in the day. Despite the broader sentiment in the market, heavyweight Samsung Electronics advanced 3.4 percent and SK Hynix edged up 0.36 percent.
The Hang Seng Index lost 1.15 percent by 3:00 p.m. HK/SIN, but held above the 30,000 mark. Mainland markets closed mixed: The Shanghai composite edged down 0.55 percent to end at 3,271.46 and the Shenzhen composite traded lower by 0.78 percent.
Down Under, the S&P/ASX 200 declined 1.01 percent to end at 5,902. All of the benchmark's sub-indexes finished the day in the red, with the exception of gold producer stocks, which rose 1.49 percent. The heavily weighted financials sub-index lost 1.13 percent as Australia's "Big Four" banking stocks edged down.
Trade concerns back in focus
While Cohn's departure date has not been announced, the development came after Trump's announcement last week that tariffs of 25 percent and 10 percent would be implemented on steel and aluminum imports, respectively. Cohn, a free trade advocate, had been against the tariffs.
The dollar slid against the safe-haven yen on the news, fetching 105.54 at 2:40 p.m. HK/SIN, after falling as low as 105.43 earlier and compared to the 106.1 handle seen at the end of the New York session.
Against the Swiss franc, which is also seen as a safe haven currency, the greenback declined to trade at $0.9365, compared to levels around the $0.94 handle seen in the last session. The dollar index, which tracks the U.S. currency against a basket of six rivals, slipped around 0.2 percent to 89.425.
The SPDR S&P 500 ETF Trust also fell 1.5 percent while U.S. stock index futures traded lower. Dow Jones industrial average futures were down 419 points during Asia afternoon trade.
Following Trump's threat that European Union car taxes could be taxed after the bloc said it would not sit idly by U.S. tariffs, one expert cautioned that tensions could continue to simmer.
"It won't end there. It is not hard to characterize current market behavior as complacent," wrote ING Chief Economist Robert Carnell in a note.
In corporate news, Japan's Kobe Steel on Tuesday said CEO Hiroya Kawasaki would resign on April 1 following a data falsification scandal. Shares of Kobe Steel were down 7.39 percent, under-performing the broader index.
Despite the broader declines seen in greater China markets, banking stocks listed on the mainland got a boost after Reuters reported on Tuesday that regulators intended to cut the proportion of funds required to cover bad debt. China Construction Bank finished the day up 1.85 percent and Industrial and Commercial Bank of China advanced 1.37 percent.
On the commodities front, oil prices moved in the same direction as stocks. U.S. crude futures lost 0.86 percent to trade at $62.06 per barrel and Brent crude futures were down 0.85 percent at $65.23.
European stocks close higher after EU threatens US with tariffs
Europe's auto stocks were among the best performers, up 0.4 percent. Renault shot up by 8 percent after Reuters reported that it was in talks with Nissan to sell most of the French government's stake in the car-maker to its Japanese alliance partner. The stock later pared those gains as traders pointed to a denial of the plans by Nissan. The auto sector was rattled recently after Trump threatened a levy on imports of European cars.
Basic resources, meanwhile, were down more than 0.3 percent, amid concerns the Trump administration will proceed with protectionist tariffs on steel and aluminum imports. Fresnillo, Randgold Resources and Hydro were the worst performers of the sector.
Looking at individual stocks, Rolls-Royce surged to the top of the European benchmark after the firm said it remained on course to meet its financial goals for 2020. The British engine-maker reported better-than-expected operating profit for 2017, sending shares more than 11 percent higher.
Cohn, Trump's top economic advisor and the former president of Goldman Sachs, announced Tuesday that he would resign following disagreement with Trump over plans to slap tariffs on steel and aluminum imports. Cohn was seen as a voice of reason in the White House and well-liked by Wall Street.
The European Union outlined a three-pronged response to proposed metals tariffs from Trump's administration Wednesday, including items such as peanut butter, cranberries and orange juice that could see higher charges in Europe.
Speaking at a press conference in Brussels, Cecilia Malmstrom, the EU's commissioner for trade, said the institution would take the case to the World Trade Organization and would coordinate its actions with other trade partners that are also against the proposed tariffs from the U.S.
In the U.K., Saudi Crown Prince Mohammed bin Salman is to begin a three-day state visit to London. He will meet U.K. Prime Minister Theresa May, Foreign Secretary Boris Johnson and senior royals at Windsor Castle. Protests against his visit are planned.
Meanwhile, a political stalemate continues in Italy as parties vie for the leadership of a governing coalition after Sunday's inconclusive election. The leader of Italy's far-right Lega – the largest party within a center-right coalition in last week's vote – has said that he is the only option for prime minister. Former Prime Minister Silvio Berlusconi has put his name forward as the "coordinator of the center-right" coalition, according to Reuters.
— CNBC's Silvia Amaro contributed to this report.+