 "Global shares dip on concerns over Ukraine, Chinese growth")
But an upbeat performance on Wall Street the previous day kept losses in check, as did expectations that US and British inflation figures later on Tuesday will be soft enough to keep interest rates at record lows for some time.
The focus in Asia was on data showing China's money supply grew at the weakest pace in more than a decade in March, in another sign of softening momentum in the world's second largest economy.
Europe's focus turned to the tense political backdrop in Ukraine, which kept investors on edge.
Ukraine's president threatened military action after pro-Russian separatists occupying government buildings in the east ignored an ultimatum to leave and another group of rebels attacked a police headquarters in the region.
US officials have said they were in talks with European partners on how to punish Moscow for what Kiev and its Western allies call a Russian plot to annex Ukraine.
"If there is any sort of announcement that there are going to be further curbs from the West, we'd expect the market to drop off again," said Stuart McDonald, a sales trader at IG.
At 0740 GMT the FTSE Eurofirst 300 index was down 0.2% at 1317 points, with brewer SABMiller, cosmetics group L'Oreal and foods giant Nestle's setting a negative tone with weak sales reports.
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In Asia, China's benchmark Shanghai Composite Index slid 1.4%, its biggest fall in almost a month, while the MSCI's broadest index of Asia-Pacific shares outside Japan lost 0.3%.
Japan's Nikkei rose 0.8%, as bargain-hunters stepped in after the index hit a six-month low on Monday.
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The main economic drivers for investors on Tuesday are likely to come from the US and UK inflation reports for March.
Britain's annual inflation is expected to fall to 1.6%, the lowest since November 2009 and likely to cool traders' bets that surprisingly strong economic growth will bring forward the timing of the first Bank of England rate hike.
Sterling was among the biggest movers on global currency markets on Tuesday, shedding 0.2% against the dollar to trade at a one-week low below $1.67.
The euro remained under pressure, down slightly at a six-day low of $1.38, on weekend comments from European Central Bank President Mario Draghi, who said exchange rate strength could trigger further policy easing.
The dollar stood at 101.81 yen, little changed from late New York trade on Monday, when it pulled away from a three-week trough of 101.32 hit late last week.
"Today's UK and US inflation reports will be friendly - i.e., low!," wrote Kit Juckes, senior currency strategist at SocGen in a note on Tuesday, adding low interest rates should continue to support asset prices and higher-yielding currencies.
US Treasuries yields were little changed from late Monday levels at around 2.64%, not far from a six-week low of 2.603% hit on Monday.
Gold fell back from its three-week high of $1,330.90 touched on Monday, trading down 1% at $1,311 an ounce, while Brent crude futures dropped a third of one% below $109 a barrel following a surge to a six-week high the previous session.