European shares fell on Tuesday, extending the previous session's steep losses in choppy trade as investors grappled with fears Spain may require a full sovereign bailout.

The FTSEurofirst 300 closed down 0.6 percent at 1,018.61, having sunk 2.4 percent on Monday on heightened worries over Spain after press reports indicated more of its regional governments could follow Valencia in requesting aid.

The IBEX 35 in Madrid dropped 3.6 percent, while Milan's FTSE MIB shed 2.7 percent to close at its lowest level since the launch of the euro.  Many see Italy as the next potential bailout candidate after Spain.

At an auction on Tuesday, Spain paid the second highest yield on short-term debt since the birth of the euro. Short-term Spanish bond yields continued to rise above longer-term yields, usually a sign that markets are pricing in a greater risk of a credit event.

"The short-term yields are going as high as the long-term, so there is no escape and very soon they will find it difficult to fund themselves in the short term too," said Manish Singh, director and head of investment services at Crossbridge Capital, which has more than $2 billion of assets under management.

Banking stocks fell sharply on concerns over their exposure to the euro zone debt crisis, with Deutsche Bank on Tuesday becoming the latest global investment bank to post weaker second quarter pretax profit, as the weak euro and lower trading activity hit earnings.

Its shares slipped 0.2 percent.

The grim backdrop was compounded by a weaker-than-expected German purchasing managers' survey, which showed private sector activity in Europe's largest economy contracting for a third straight month.

And there was an even worse picture for the overall euro zone's private sector, which shrank for a sixth month in July as manufacturing output nosedived, adding to the likelihood that the bloc will slump back into recession.

Greece also provided cause for concern, as inspectors from the troika, the trio of international lenders keeping the country afloat, returned to Athens to relaunch its stalled economic plan.

The officials from the International Monetary Fund, European Commission and European Central Bank must decide whether to keep the nation hooked up to a 130-billion-euro lifeline or let it go bust.

"One day markets focus more on the negative side on Spain and Greece, and on others they focus more on the potential of new capital injections, and this will make for a very nervous and volatile summer," said Philippe Gijsels, head of research at BNP Paribas Fortis Global Markets.

"I'm certainly not wildly bullish - I think there is quite a bit of worry out there. But on the other hand we also caution clients not to be too negative ... it's extremely difficult to position."