There were falls of almost 2% on South Korea's Kospi and Hong Kong's Hang Seng, with markets in mainland China and Australia also down - taking their cues from sharp losses on Wall Street earlier.
The so-called fear gauge - the CBOE Volatility Index (VIX), the most widely followed barometer of expected USA stock market volatility, hit its highest since November 8, when Mr Trump was elected president.
Kathleen Brooks, research director at City Index Direct, said: "The Swiss franc is the safe haven of choice today as risk sentiment gets hit from escalating nuclear fears between the United States and North Korea".
Seven of the 11 major S&P 500 sectors were higher, with the technology's 0.36% rise leading the advancers.
The Dow Jones US Defense Index increased +1.61% in trading today, over one year the index has gained 23% compared to Dow Jones Industrial Average of 18.97%.
Geopolitical concerns contributed to the continued strength among treasuries amid an ongoing escalation in tensions between the US and North Korea.
The tentative gains "suggest that the headline shock value pertaining to the US-North Korea standoff is starting to dissipate, which is to say actual action will now speak much louder than words", said Briefing.com analyst Patrick O'Hare.
Federer cruises into Montreal semi-finals
Prior to this, the pair had met only once during a Davis Cup World Group play-off in 2012, when Federer clinched a 6-1, 6-4, 6-4 win.
With the tense mood pushing European shares down for a third day and Wall Street set to fall again, global stocks were on course for their worst week since Donald Trump won November's election.
As of 12:20 BST, the FTSE 100 index had lost 83 points to stand 1.12 percent lower at 7,306.94, staying on track to post a near three-percent loss for the week. Stocks in Taiwan, Singapore and other Southeast Asian countries were also lower.
The strength on Wall Street is partly due to bargain hunting, with traders picking up stocks at reduced levels following the pullback seen over the past few sessions. "This is mainly due to the fact that in the event of a crisis involving the U.S. directly, investors are more likely to seek refuge in an asset like gold which bears no country risk and also benefits when the dollar depreciates", Gambarini writes. Spot gold added 1.3 percent to $1,277.15 an ounce.
On Thursday, North Korea's state media kept up its anti-U.S. rhetoric, saying the nation will develop a plan by mid-August to launch intermediate-range missiles at Guam.
The Nasdaq Composite was up 19.35 points, or 0.31%, at 6 236.22.
A Labour Department report showed its producer price index posted a surprise drop in July, down 0.1 percent for the largest slide in nearly a year. The S&P has lost more than 1 percent on only three days this year.