The euro, which hit its highest since the start of 2015 on August 2, dipped 0.2 percent to $1.1753 in early trade in Europe.
The president said "things will happen to them they never thought possible" should Pyongyang attack the United States or its allies. This is because bond prices and yields have an inverted relationship.
The market's main backstop in times of strain, gold, hit a two-month high of $1,282 an ounce amid the nervousness.
He said: "The response that the North Korean nation was considering a missile strike on the USA base in Guam was the equivalent of a two fingered response to the U.S. president, and there is a danger that this war of words between two leaders with large egos could get out of control".
The market also awaited U.S. consumer inflation data on Friday that would offer more clues about the pace of the U.S. Federal Reserve's monetary tightening.
In Australia, the S&P/ASX 200 advanced 0.41 percent, with the index driven by broad-based gains, with only the energy and utilities sub-indexes registering slight losses. The Shanghai Composite Index lost 0.2 percent to 3,273.71 and Hong Kong's Hang Seng was off 0.2 percent at 27,803.55. The yellow metal traded at $1,285.64 an ounce at 9:53 a.m. HK/SIN, a tad below the $1,285 level seen Thursday. The benchmark Kospi tumbled 39.76 points or 1.7% to 2,319.71, its lowest level since May 24th.More news: Tony Pulis signs two-year contract extension with West Brom
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Oil prices are holding their own ahead of the U.S open after yesterday's weekly API inventory reported a large drop in U.S crude stocks countered balanced industry doubts that compliance with OPEC-led supply cuts will increase. The USD/JPY pair was trading at 110.072 Yen, up 0.13%.
Innogy shares have moved to the downside after German utility maintained the outlook on the current year's business performance after reporting a drop in first-half net income to 817 million euros from 1.08 billion euros last year.
Data overnight from China showed that China's producer price gains held steady on surging commodity prices, as demand stayed resilient and the government's drive to reduce industrial capacity takes hold.
Japan's Nikkei 225 rose 0.08 percent, but was off session highs seen earlier.
The US Consumer Price Index (CPI) edged up 0.1% last month after staying flat in June and falling by 0.1% in May. Despite the losses, Noble shares rose 17.14 percent.
"Risk-off sentiment dominates Asian markets into the end of the week with President Donald Trump's words still sending shockwaves into the markets", said Jingyi Pan, market strategist at online trader IG.