Milan's stock market was the worst performer in Europe, sinking by 1.2 percent as Italian debt concerns returned to the fore.
"Italy is once again becoming a problem for the eurozone," noted analyst Konstantinos Anthis at trading firm ADSS.
However, losses were capped elsewhere after a much-feared surge in populist groups largely failed to materialise in European Parliament elections.
Although voters shifted allegiances in the EU elections, mainstream parties managed to retain control.
London stocks dipped 0.2 percent following a long holiday weekend, while Frankfurt shed 0.5 percent and Paris was down 0.6 percent.
- 'Political fight' -
=====================
"European stock markets are in the red as Italian government bond yields have ticked up over a fear for a political fight between Rome and Brussels," said analyst David Madden at CMC Markets UK.
"The EU has warned the Italian government they could be fined... for failing to curb their debt levels, and Italy's joint deputy prime minister Matteo Salvini declared he will use 'all his energies' to fight the EU's rules."
Salvini said Tuesday he expected Brussels to slap Rome with a three billion-euro ($3.36 billion) fine over the country's rising debt and structural deficit levels.
"At a time when youth unemployment touches 50 percent in some regions... someone in Brussels is demanding, under the old rules, a fine of three billion euros," he told RTL 102.5 radio.
"All my energy will go into changing these rules from the past," said Salvini, who has been emboldened after his far-right League party won Sunday's European Parliament elections in Italy.
The European Commission is expected to start disciplinary steps against Italy on June 5 by opening an excessive deficit procedure which could hand Italy a fine of up to 0.2 percent of the nation's GDP.
Italy's public debt is a big problem, sitting at 132.2 percent of the country's GDP in 2018 -- way above the 60 percent EU ceiling.
- Brexit Party triumphs -
=========================
In Britain, the pound continued to languish near recent lows after the anti-EU Brexit party topped European polls in Britain, putting intense pressure on the ruling Conservatives who suffered a historic rout -- and raising the chances of a no-deal departure from the EU at the end of October.
British Prime Minister Theresa May's Conservatives finished fifth with nine percent -- their worst performance since 1832 -- and the main opposition Labour Party was also punished for not clearly spelling out its Brexit stance.
David Cheetham, analyst at broker XTB, said the outcome was "providing a headwind to any recovery for the pound.
In Asia, markets mostly rose Tuesday as US President Donald Trump took a softer approach in Washington's trade dispute with Japan as he wrapped up his visit to the Asian ally.
Trump's visit comes as a trade row between Washington and Beijing escalates -- with no date set for tariff negotiations to resume.
Elsewhere, oil prices rose after last week's heavy plunge that followed a surprise increase in US crude and gasoline inventories. Rising stockpiles tend to indicate weaker demand for black gold.
- Key figures around 1045 GMT -
===============================
Milan - FTSE MIB: DOWN 1.2 percent at 20,110.50 points
London - FTSE 100: DOWN 0.2 percent at 7,264.65
Frankfurt - DAX 30: DOWN 0.5 percent at 12,013.73
Paris - CAC 40: DOWN 0.6 percent at 5,304.91
EURO STOXX 50: DOWN 0.7 percent at 3,340.45
Tokyo - Nikkei 225: UP 0.4 percent at 21,260.14 (close)
Hong Kong - Hang Seng: UP 0.4 percent at 27,390.81 (close)
Shanghai - Composite: UP 0.6 percent at 2,909.91 (close)
New York - Dow: Closed for holiday Monday
Euro/dollar: DOWN at $1.1187 from $1.1194
Dollar/yen: DOWN at 109.33 yen from 109.51 yen
Pound/dollar: DOWN at $1.2666 from $1.2679 at 2050 GMT
Euro/pound: UP at 88.31 pence from 88.28
Oil - Brent Crude: UP 14 cents at $70.25 per barrel
Oil - West Texas Intermediate: UP 44 cents at $59.07