There were falls of nearly 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.
Global political tensions have seen investors sell off shares as they flee to less risky assets such as the yen and the Swiss franc.
The FTSE's fall was led by the volatile mining sector, with London-listed global commodity firms such as Antofagasta, Rio Tinto, BHP Billiton and Anglo American among the biggest losers.
Markets in Italy, France and Germany also saw declines.
Simmering tensions between the US and North Korea have come back to the boil in recent days after Pyongyang disclosed plans to fire missiles over Japan to land near America's Pacific territory of Guam.
Mr Trump warned Kim Jong Un earlier this week that his country faced "fire and fury".
He has now gone further, saying the warning may not have been tough enough and that if North Korea did what it had threatened, it faced "an event the likes of which nobody's seen before".
Until now, investors have broadly felt able to brush off the rhetoric as sabre-rattling.
But the increasingly bellicose atmosphere, driven by unpredictable leaders on both sides, has seen anxiety escalate.
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 US and North Korea have intensified to the point that markets can't ignore it."
He said the crisis provided a "perfect trigger" for a correction at a time when many markets - including the FTSE 100 - were at or around record highs, leaving them vulnerable to a sell-off if investors think it is time to take profits.
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