Oil prices edged up after France launched large-scale air strikes against Islamic State targets in Syria.
Asian shares fell to their lowest in six weeks but European shares' losses were modest as markets reopened after the attacks that killed more than 130 people.
U.S. stock index futures turned positive, indicating Wall Street was likely to open slightly higher.
"It seems likely that -- at least temporarily -- risky assets, that were under pressure anyway, continue to trade with a weaker tone," RBC's chief European macro strategist Peter Schaffrik said.
The pan-European FTSEurofirst 300 index opened lower, dragged down by travel and leisure stocks, though miners and energy stocks gained. The index was last down 0.04 percent.
MSCI's broadest index of Asia-Pacific shares outside Japan fell nearly 1.5 percent at one stage, its biggest daily fall since Sept. 29, and was last down 1.3 percent.
Leading the losers was Japan's Nikkei stock index which tumbled nearly 1.1 percent, nearly wiping out last week's gains as data showed the economy slipped back into recession in the July to September quarter.
It contracted at a 0.8 percent annualized rate. Economists polled by Reuters had forecast a 0.2 percent contraction.
Emerging market stocks lost 0.9 percent.
The widely-tracked CBOE volatility index or "fear gauge" hit its highest level since Oct. 2.
Chinese stocks bucked the trend, however, reversing early losses to end higher. The CSI300 index of the largest listed companies in Shanghai and Shenzhen rose 0.5 percent while the Shanghai Composite Index gained 0.7 percent.
Yields on safe-haven two-year German bonds hit a new record low of -0.382 percent before edging up to -0.37 percent. Ten-year German yields, the benchmark for euro zone borrowing costs, fell 1.2 basis points to 0.55 percent.
U.S. Treasury yields also fell. Ten-year yields were last down 2.1 bps at 2.59 percent, having hit 2.41 percent in Asian trade.
In currency markets, the euro hit a 6 1/2-month low against the safe-haven yen, and close to that mark versus the dollar, before recovering somewhat. The Swiss franc, also sought in times of turmoil, strengthened against the euro.
The single currency was last down 0.4 percent at $1.0740, having hit $1.0674 last week on expectations the European Central Bank will step up monetary easing.
"There is some caution ruling markets as we have seen with the reaction to stock markets. Ultimately, the Fed/ECB divergence will be the focus, with markets already pricing in a 10 basis point deposit rate cut by the ECB and extension of the QE program," said Manuel Oliveri, FX strategist at Credit Agricole.
The dollar was flat against a basket of major currencies
Markets in the Middle East, which trade on Sunday, were hit hard, though part of that decline was due to last week's drop in oil prices. Saudi Arabia's stock index hit a 35-month low on Sunday while stocks in Dubai and Egypt hit their lowest of the year.
Crude oil rose. Benchmark Brent rose 20 cents, or half a percent, at $44.68 a barrel, having dropped 1 percent on Friday. Traders said the rise was largely a matter of sentiment, with a premium being factored in after French strikes in Syria in response.
Spot gold rose 1 percent. It last traded at $1,092.70 an ounce, having hit its lowest since February 2010 on Thursday.