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Europe shares end higher; Lufthansa hit by plane crash

European equities finished higher on Tuesday, rising from session lows, as investors reacted to fresh economic data from the euro zone.

The pan-European Euro Stoxx 600 index closed around 0.3 percent higher, having starting the session lower.

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Shares of Airbus, closed around 0.6 percent higher, having fallen as much as 2 percent on Tuesday after an A320 passenger plane had crashed in the south of France.

The plane was operated by Germanwings, a budget airline owned by Lufthansa. Shares of the German carrier sunk by as much as 4.6 percent, before closing 1.7 percent lower.

Read MoreAirbus plane crashes in Southern France

PMI data beats

Meanwhile, new data on Tuesday morning showed that business activity in the euro zone hit a 46-month high in March, bolstering hopes that growth in the region is becoming more entrenched.

Germany's Purchasing Managers' Index (PMI) figures beat market expectations, with business activity in the country growing at its highest rate in eight months.

The data also showed France's private sector had expanded for a second straight month.

Germany's DAX index closed around 1 percent higher; France's benchmark CAC was roughly 0.8 percent higher.

Read MoreEuro zone business activity shoots up

"This is a highly encouraging and positive set of euro zone purchasing managers' surveys, and it is welcome to see that manufacturing activity is now gaining appreciable in addition to healthy services activity," Howard Archer, an economic at IHS Global Insight, said in a research note.

"It is not just the headline figures that are encouraging, but the whole tone of the surveys."

Markets had started the session weaker, after disappointing manufacturing data out of China prompted concerns of slower growth for the world's second largest economy. China's HSBC flash PMI for March fell to 49.2, an 11-month low.

U.S. stocks traded in a narrow range on Tuesday, as investors weighed up a stronger-than-expected new home sales number, an in-line inflation report and continued consolidation in currency and energy price movements.

Greece in focus

On Tuesday morning, a Greek government official said that the country was going to present a reform package to the Eurogroup of finance ministers by next Monday at the latest, Reuters reported.

This came after Greek Prime Minister Alexis Tsipras met German Chancellor Angela Merkel in Berlin on Monday.

Read MoreGreece and Germany—all talk and no action?

The Athens composite index closed around 3.7 percent higher on Tuesday.

British finance minister George Osborne said on Tuesday that the risk of Greece leaving the euro zone was rising because of the rancor between Athens and the rest of the currency union, according to Reuters.

"The risks of Greece leaving are rising, because the ill-will round the table is palpable between the euro zone and Greece," Osborne told members of parliament.

Also in the U.K., the consumer price index showed price rises at a record low of zero percent on the year before in February.

The benchmark FTSE 100 finished provisionally down 0.1 percent, having touched a record high during the trading session, according to Reuters.

In individual stocks news, petroleum and chemicals firm Rubis climbed to finish over 5 percent higher 2.3 after a target price