The dollar edged up against a basket of major currencies but lost ground against the safe-haven Japanese yen. Gold, another asset sought in uncertain times, also rose.
In emerging markets, the South African rand fell more than 1 percent against the dollar and bank shares fell after S&P Global cut its credit rating to junk on Monday.
According to Reuters, the pan-European STOXX 600 share index edged up 0.1 percent, after falling from a 16-month high on Monday.
Britain's FTSE 100 index rose 0.5 percent.
Shares have hit record highs across the globe in recent months, partly in anticipation of Trump cutting taxes, easing regulation and raising infrastructure spending.
However, Trump's struggles to push other legislation through Congress has led some to question whether he will be able to fully make good on his campaign pledges.
Data on Monday showing U.S. car sales lagged market, which helped push Wall Street lower, and geopolitics, including the Russian metro blast and Trump comments on North Korea, also weighed on markets.
Automaker stocks were the main drag on Tokyo shares on Tuesday; the Nikkei fell 0.9 percent to a 10-week low, also hit by the impact of the strong yen on exporters.
MSCI's broadest index of Asia-Pacific shares outside Japan fell 0.3 percent, having hit a 21-month high last week.
Yields on low risk U.S. and German government bonds fell. falls. Benchmark 10-year U.S. Treasury yields were down 2 basis points at 2.33 percent after falling as low as 2.31 percent, its lowest in more than a month, in Asian trade.
German 10-year yields touched their lowest level since March 1 and last stood at 0.26 percent, down 1.6 bps.
Italy's bonds outperformed the rest of the euro zone on the prospect of help for two struggling Italian lenders.
Yields on the bonds of Banca Popolare di Vincenza and Veneto Banca fell sharply after a European Commission spokesperson said late on Monday said there could be a solution on a bailout.
Italian 10-year government bond yields fell 2.7 bps to 2.3 percent.
"Italy's banking sector has been a never-ending story, so any news pointing towards state support reduces the risk of a more severe development that could be the beginning of a banking crisis," said DZ Bank strategist Daniel Lenz.
The dollar inched up 0.1 percent against its currency basket but fell 0.4 percent to 110.44 yen, off a low for the day of 110.32 yen.
"(The yen buying) is based on broad-based risk-off since yesterday. There was a tragedy in Russia and there may be some hedging-type buying ahead of the French presidential debate and also French elections in three weeks," said Yujiro Gato, currency analyst with Nomura in London.
The euro fell 0.2 percent to $1.0652 and sterling fell 0.5 percent to $1.2428.
The Australian dollar was 0.6 percent weaker at $0.7555 after the central bank held rates steady at a record low 1.5 percent as expected, and said growth in household borrowing, largely for housing, was outpacing rises in household income.
South Africa's rand fell as much as 1.9 percent before recovering to trade down 1.1 percent at 13.83 per dollar while bank shares tumbled after the credit rating cut in response to President Jacob Zuma's dismissal of his finance minister, Pravin Gordhan, last week.
Yields on South African dollar-denominated government bonds rose, with the 10-year benchmark yielding nearly 5 percent.
Gold hit a one-week high around $1,260 an ounce.
Oil prices fell, hit by a rebound in Libyan crude production and an increase in U.S. drilling. Brent crude fell 21 cents a barrel to $52.92.