Trump's warning came as a United States naval strike group headed towards the Korean peninsula, a show of force that prompted the nuclear-armed North to declare it was "ready to react to any mode of war desired by the US". Tensions are rising over North Korea, which threatened the US against making any military moves after Washington sent an aircraft carrier to the divided Korean Peninsula.
Trump also lashed out at North Korea on Twitter on Tuesday, urging China to do more to rein in its communist neighbor.
The broader Topix fell 1.1 percent to 1,462.60 and the JPX-Nikkei Index 400 was down 1.2 percent to 13,114.20.
European shares were bolstered as Daimler AG results lifted automakers.
Shanghai nudged 0.4 percent lower.
ASIA'S DAY: Japan's benchmark Nikkei 225 added 0.7 percent to finish at 18,797.88, while Australia's S&P/ASX 200 gained 0.9 percent to 5,912.90. Hong Kong's Hang Seng Index was in similar territory, declining by 0.31 percent.
"Gold and the Japanese Yen have strengthened as mounting geopolitical tensions continue to weigh on markets", said dealers at HiFX, in a note.
Investor worries over Syria and North Korea sent gold and 10-year Treasury yields to their best levels since November overnight.
"Geopolitical risk can be a potentially positive factor for the yen, with risk aversion and flight to safety", said Masafumi Yamamoto, chief currency strategist at Mizuho Securities in Tokyo.
At the same time, tensions between the US and Russian Federation simmered following last week's USA cruise missile strikes on a Syrian air base. The dollar/yen traded at 109.65 at 9:35 HK/SIN time, after trading at the 111 level earlier in the week.
Energy companies led USA stock indexes to modest gains in afternoon trading Monday as the price of crude oil headed higher for the fifth day in a row.
The sell-off of the company's stock came as an analyst warned it may lose a contract with tech giant Apple. That pushed up shares in major mining companies: Fresnillo was up 2.4 percent and Randgold Resources 2.3 percent higher in London.
OIL: Benchmark crude oil was headed higher for the fifth day in a row.
Oil prices held firm at $52.36 per barrel, on risks that the Syria conflict may spread more widely within the oil-rich Middle East region. Australian shares were also stronger, up 0.7 percent at a near two-year high as higher oil and metal prices propped up commodity plays. Last week API reported a draw in crude stocks, while EIA reported a build.
Yields on USA government bonds plunged overnight as geopolitical headwinds accelerated amid a continuing rethink on Trumpflation, signalling the potential for still lower yields at least in the short term. France's CAC 40 gained 0.4 percent to 5,123.01 and Germany's DAX added 0.4 percent to 12,183.46.
The Bank of Japan said that producer prices were up 0.2 percent on month in March - shy of expectations for a gain of 0.3 percent, which would have been unchanged from February following an upward revision from 0.2 percent.