On the 1,000th day of Russia's offensive on Ukraine, Moscow said it will consider using the weapons against a non-nuclear state if they are supported by nuclear powers.
Russia vowed also to defeat its neighbour.
"Investors are once again turning cautious on fears of further escalation," said Chris Beauchamp, chief market analyst at trading platform IG.
The Paris and Frankfurt stock markets were down nearly 1.5 percent in midday deals. London fared better, with a drop of 0.4 percent.
The dollar was mixed against main rivals, while there were gains for other investments seen as havens, notably gold and the yen.
Russia's move comes days after the United States granted permission for Ukraine to strike Russian territory with American-supplied long-range missiles.
In Asia on Tuesday, Hong Kong and Shanghai stock markets closed higher on hopes China will unveil more stimulus aimed at kickstarting its economy and property sector in particular.
On the corporate front, shares in German industrial giant Thyssenkrupp rose about six percent after the group said it expected a return to profit in its next fiscal year.
It comes after the group reported a massive annual loss for 2023-2024.
Nestle dropped 1.5 percent after new chief executive Laurent Freixe announced a plan to slash costs and have a standalone water and beverages business.
Equities have seen big swings since Donald Trump was elected US president earlier this month, as markets weigh renewed inflation risks from his pledge to cut taxes and impose import tariffs.
That has also given a headache to policymakers at the US Federal Reserve who are still fighting to bring prices under control.
Traders are scaling back their bets on how many more interest-rate cuts the Fed will announce in the coming year.
There is also a fear that Trump's second term will see another debilitating trade war with China as the country battles against slowing growth.
US stocks finished mixed Monday, with traders bracing for Nvidia earnings this week, and piling into Tesla on press reports that Trump could ease regulation on self-driving vehicles.
- Key figures around 1115 GMT -
London - FTSE 100: DOWN 0.4 percent at 8,079.48 points
Paris - CAC 40: DOWN 1.4 percent at 7,197.49
Frankfurt - DAX: DOWN 1.3 percent at 18,986.54
Tokyo - Nikkei 225: UP 0.5 percent at 38,414.43 (close)
Hong Kong - Hang Seng Index: UP 0.4 percent at 19,663.67 (close)
Shanghai - Composite: UP 0.7 percent at 3,346.01 (close)
New York - Dow: DOWN 0.1 percent at 43,389. points (close)
Euro/dollar: DOWN at $1.0563 from $1.0600 on Monday
Pound/dollar: DOWN at $1.2641 from $1.2678
Dollar/yen: DOWN at 153.83 yen from 155.04 yen
Euro/pound: DOWN at 83.54 pence from 83.57 pence
West Texas Intermediate: DOWN 0.5 percent at $68.81 per barrel
Brent North Sea Crude: DOWN 0.4 percent at $72.98 per barrel
dan-ajb/bcp/kjm
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