While the German DAX Index rose by 0.3 percent, the French CAC 40 Index and the U.K.'s FTSE 100 Index edged up by 0.2 percent and 0.1 percent, respectively.
Financial markets have tended to quickly shake off North Korea's periodic saber-rattling in the past, dismissing it as bluster, but tensions have lingered this year amid signs that it is making progress in its ballistic missile program and on Trump's growing frustration with Pyongyang.
US stocks closed lower on Tuesday after Trump's vow to respond aggressively to any North Korean threats triggered a late afternoon selling spree.
Tokyo´s blue-chip index tumbled 1.3 percent to its lowest close since late May after the Dow´s winning streak of nine straight records ended following Trump´s sharp rhetoric of "fire and fury", with the main European bourses also opening lower Wednesday.
"Geopolitical tensions are the key driving force this morning, boosting demand for safe havens", TD Securities analysts said in a note.
Shortly after Trump made his remarks, North Korea said it was "carefully examining" the idea of a missile strike on Guam, a U.S. Pacific territory.
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Among oil stocks, Woodside Petroleum is down 0.4 percent and Santos is losing 0.6 percent, while Oil Search is adding 0.3 percent after crude oil prices slipped overnight. Major indexes in China, Japan, and India were also lower. Chinese blue chips closed flat but Hong Kong's Hang Seng index was last down 0.2 percent. The dollar was down 1.2 percent at 0.9627 Swiss francs, while an ounce of gold was 1 percent higher at $1,275.
As reported at 10:55 am (JST) in Tokyo, the USD/JPY was trading at 109.823 Yen, down 0.45%; the pair earlier hit a trough of 109.793 Yen, while the session peak stands at 110.386 Yen. The jump in the franc after the Brexit vote in June past year was bigger than today's upward lurch on fears of a nuclear conflict.
Yields on core government debt fell.
"Obviously we are looking at the increased tensions between the USA and North Korea", said Brad Bechtel, managing director FX at Jefferies in NY.
Oil prices nudged higher with global benchmark Brent Crude up 0.65%, and USA benchmark West Texas Intermediate up 0.61% recently after OPEC made a decision to extend output cuts by nine months to March 2018.