On Friday, Donald Trump said the US military was "locked and loaded" to deal with North Korea,
By mid afternoon, the FTSE 100 was down 71.50 points, or 1%, to 7,318.44, having dropped 1.4% on Thursday.
Other markets in Europe also fell, with Germany's Dax index down 0.1% and France's Cac 40 dropping 1.1%.
US markets held steady in early trade on Friday, with the Dow Jones edging up 0.1%.
On the London stock market, mining shares saw the biggest falls as many metal prices were hit by the geopolitical concerns. Shares in Glencore, Rio Tinto and Anglo American were all down by more than 3%.
"The FTSE has carried on where it left off on Thursday, with yet another day of risk-off sentiment seeing investors shift out of equities," said Joshua Mahony, market analyst at IG.
"The UK headline index has crashed to the lowest level since late June, in a week which has turned from mundane to insane.
"For a week that has been largely devoid of major economic releases, Donald Trump's confrontational stance with North Korea has raised volatility across the board."
Gold - generally regarded as a safer asset in times of uncertainty - hit its highest price for more than two months on Friday, touching $1,288.97 an ounce at one point.
On the currency markets, the pound was unchanged against the dollar at $1.2972 and down 0.3% against the euro at 1.0992 euros.
The UK's stock market has fallen 1% as worries over the situation between the US and North Korea continue to rattle investors.