Mr Trump's threat earlier this week, to unleash "fire and fury" on Pyongyang if it attacked, was ultimately dismissed as bluster by many investors.
Against the Swiss Franc, the dollar erased earlier losses to traded little changed on the day.
"What has changed this time is that the scary threats and war of words between the United States and North Korea have intensified to the point that markets can't ignore it", said Shane Oliver, head of investment strategy at AMP Capital in Sydney, as quoted by Reuters.
"The typical text book trade is that investors rush for safe havens".
Wall Street closed sharply lower, with Dow Jones down over 200 points on Thursday.
The CBOE Volatility Index, the most widely followed barometer of expected near-term stock market volatility, ended at a session low of 11.11 after rising as high as 12.63. North Korea also laid out detailed plans of how it would launch a missile strike on USA military bases in Guam.More news: Barcelona warned over Messi's £271m release clause
The dollar index, which measures against a basket of currencies, fell 0.05 percent. However, it also showed compliance by OPEC members to the output deal decreased to 86% in July from 96% in June, and higher production from Libya and Nigeria led to an overall increase in OPEC's total output in July. The US currency was down 0.3 per cent at 109.94 yen, following a retreat to 109.740, its weakest since June 15th. Hong Kong's Hang Seng added 0.6 percent to 27,854.91, while the Shanghai Composite inched up almost 0.1 percent, to 3,281.87.
Instead, investors turned to assets that tend to benefit in times of geopolitical and financial stress. It was down 0.2% at 108.98 yen, after retreating 0.7% yesterday.
Japan is the world's biggest creditor country and there is an assumption that investors there will repatriate funds in a crisis.
The Korean won continued to fall versus the dollar, down 0.13 per cent to 1,143.5 on Friday for a 1.6 per cent decline on the week. The Swiss currency was also on track for its biggest daily gain against the euro since the Swiss National Bank removed its cap on the currency in January 2015. It is poised to end the week down 1 percent.
"Heightened geopolitical risks overnight have seen the markets flip from risk-on to risk-off and we have to wait and see how long this move runs before adding some positions", said Viraj Patel, an FX strategist at ING in London.
The dollar was further weighed Friday by the soft US inflation data.More news: Guardiola defends Man City's big spending
Yields on core government debt fell.
Benchmark 10-year notes last rose 5/32 in price to yield 2.2255 percent, from 2.242 percent late on Wednesday.
Spot gold rose 0.5 percent to $1,266.20 per ounce at 0054 GMT.
Shane Oliver, head of investment strategy at AMP Capital in Sydney, said: "What has changed this time is that the scary threats and war of words between the U.S. and North Korea have intensified to the point that markets can't ignore it". It is trading at its best level in two months, and is threatening to crack the $US1,300 level for the first time since the day following the United States presidential election.
In oil, the price of Brent crude sunk by 0.5% to 51.65 USA dollars a barrel amid concerns about over supply in the market.More news: East Harling murder: Man held over Peter Wrighton stabbing
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