Technical strategists, however, said it was too soon to call the end of the downward trend, with the latest move likely to prove just a temporary correction.
By 1028 GMT, the FTSEurofirst 300 index was up 1.0 percent at 1,042.44 points, extending gains into a second day.
The Euro STOXX 50 index of euro zone blue chips added 1.6 percent to 2,337.11 points, bouncing from technical support of 2,300 after languishing in oversold territory on the 7-day relative strength index (RSI) for around two weeks. The index is still down some 11 percent in the past month.
Since the middle of March, we have gone through quite a downward movement. The index fell below the 100- and 200-day moving averages. We are now seeing a stabilisation but it will take time before we really make a new attempt at the upside, said Petra Kerssenbrock, technical strategist at Commerzbank, adding that the rebound could run out of steam in the 2,350-2,366 area.
Implied volatility on the Euro STOXX 50, a crude barometer of risk aversion, eased to 27.12 - its lowest in over a week but still up nearly 50 percent since mid-March.
Banks, which tend to be the most sensitive both to broad investor sentiment and directly to swings in sovereign debt concerns due to their exposure there, were among the biggest gainers, up 2.7 percent.
Investors were reassured by Spain raising its target amount, albeit paying high yields, at an auction of short-term Spanish debt, seen as a litmus test for a sale of long-term paper on Thursday as Madrid strives to shore up its finances and avoid an international bailout.
Spain's IBEX was 1.0 percent higher, recovering from a fresh 3-year low set in early trading despite a slump in one of its biggest stocks, Repsol on news that Argentina was set to re-nationalise its YPF unit.
The Spanish oil major fell 6.8 percent, the biggest loser on the FTSEurofirst 300.
The broader market, though, took heart from an unexpected jump in the German ZEW economic sentiment index to its highest level since June 2010, which suggested that Europe's biggest economy has not yet been hit by the fallout from debt woes in some of its euro zone partners.
Germany remains an outperformer as a major exporter, the country benefits from any positive news coming from world trade, said Benoit Peloille, equity strategist at Natixis.
The DAX was up 1.1 percent on Tuesday, taking its year-to-date gains to over 13 percent, against a broadly flat showing on Euro STOXX 50.
Longer-term though, analysts cautioned that the strong German sentiment was not reflected in hard economic data while the Spanish debt demand came at the price of much higher premiums than in previous tenders.
The over-arching theme in equity markets is still the re-ignition of the tensions in financial markets on euro zone concerns, and this is something that may stay with us for some time, Gerhard Schwarz, head of equity strategy at Baader Bank, said.