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While the euro remained under pressure as German Chancellor Angela Merkel struggled to form a coalition government, Frankfurt's DAX pushed 0.8 per cent higher.
The leader of 12 years indicated on Monday she was ready to hold snap elections after the collapse of talks at the weekend shoved Europe's biggest economy toward political turmoil.
"Merkel said she did not favour a minority government because it wouldn't bring the stability necessary to govern effectively," said Greg McKenna, chief market strategist at AxiTrader.
"That suggests more talks but an increased chance of fresh elections in early 2018. How that plays out is going to be interesting for the euro and certainly the Brexit process as well."
Financial analyst Connor Campbell at Spreadex said "it seems investors have faith that Germany will find a way to move past its current uncertainty without the kind of performance-damaging aftermath seen by some of its peers" such as Spain and the UK.
Shares in carmakers helped drive the DAX higher, with Volkswagen accelerating 3.0 per cent after the company was more optimistic about earnings thanks to an offensive on SUVs.
BMW rose 1.9 per cent and Daimler gained 1.6 per cent.
In Paris, the CAC 40 ended the day 0.5 per cent higher, while the FTSE 100 in London added 0.3 per cent.
EasyJet's share price shot up 5.1 per cent despite annual net profit dropping by almost one third at the British no-frills airline on strong competition and a Brexit-fuelled slump in the pound.
However, investors were pleased with "signs of a break in the clouds ahead", noted George Salmon, equity analyst at stockbroker Hargreaves Lansdown.
"Forward reservations are up on last year, and the trend for rising costs and lower prices is set to reverse in the coming months."
Across the Atlantic, while concerns about the prospects for US tax reform continue to nag, optimism about the global economy provided some buoyancy to Wall Street.
The Dow was up 0.7 per cent in late morning trading.
However, with the Thanksgiving holiday shortening the US trading week analysts do not expect New York to provide many strong leads to the market in the next few days.
Tokyo's main stocks index jumped 0.7 per cent on Tuesday, led by exporters.
Among other markets, Hong Kong pushed to a 10-year high, with Tencent up 2.4 per cent, extending Monday's surge that makes it the first Asian member of the exclusive club of global firms with a market capitalisation above US$500 billion.
The Chinese internet giant was about US$520 billion, around the same as Facebook.
On currency markets, the embattled Turkish lira struck a record low against the US dollar as investors took fright over an impending trial in the United States and changes to banking regulations.
The Turkish lira lost over one percent in value to trade at 3.97 to the dollar late morning, testing the never-before-reached 4.0 ceiling, before rallying slightly to 3.95 in the early evening.
Key figures around 1630 GMT:
London - FTSE 100: UP 0.3 per cent at 7,411.34 points (close)
Frankfurt - DAX 30: UP 0.8 per cent at 13,167.54
Paris - CAC 40: UP 0.5 per cent at 5,366.15 (close)
EURO STOXX 50: UP 0.5 per cent at 3,579.18
New York - DOW: UP 0.7 per cent at 23,601.72
Tokyo - Nikkei 225: UP 0.7 per cent at 22,416.48 (close)
Hong Kong - Hang Seng: UP 1.9 per cent at 29,818.07 (close)
Shanghai - Composite: UP 0.5 per cent at 3,410.50 (close)
Euro/dollar: UP at US$1.1741 from US$1.1733 at 2140 GMT
Pound/dollar: UP at US$1.3238 from US$1.3235
Dollar/yen: DOWN at 112.38 yen from 112.64 yen
Oil - Brent North Sea: UP 10 cents at US$62.32 per barrel
Oil - West Texas Intermediate: UP 34 cents at US$56.76
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