The pan-European STOXX 600 index rose 3.1pc to its highest level in nearly a month, with Spanish and Italian stock surging 3.4pc and 4.5pc, respectively, on a slowdown in new infections in Italy, Spain and hard-hit parts of the United States.
"We see this rally as a necessary part of price discovery and finding a new bottom," said Andrea Cicione, head of strategy at TS Lombard in London.
"The initial stage was the shock and we've gone through that when the market was selling off every day. We are now transitioning to phase two, which is the consequences of the lockdowns."
The benchmark STOXX 600 index has gained more than 22pc since hitting an eight-year low in March - technically marking a bull market - but remains 24pc below its February record high, when the global spread of the coronavirus led to a virtual halt in business activity.
France's Thales on Tuesday became the latest big company to slash dividend and suspend profit forecasts, but its shares rose 3.8pc after it added a new 2 billion euro ($2.17 billion) credit facility to shore up liquidity.
German shares surged 4.5pc to their highest since March 11, as data showed industry output in Europe's manufacturing powerhouse rose by a better-than-expected 0.3pc in February, before the pandemic prompted sweeping lockdowns.
However, analysts said output will likely tumble in the next three months with the Ifo institute's index for production expectations logging its biggest drop since the survey was first conducted in 1991.
With a slate of companies withdrawing their financial forecasts and supply chains far from being revived, economists polled by Reuters said a global recession was under way, although most clung to hopes of a swift rebound.
"No one yet knows the exact damage this virus has already done to the global economy and corporate earnings, and what kind of exit strategies countries will follow in the weeks ahead," said Hussein Sayed, chief market strategist at FXTM.
"The road ahead won't be a smooth one, especially as investors still need to digest a mountain of negative economic data and possibly many bankruptcies."
A Reuters report said Germany's Lufthansa will discuss permanently grounding its Germanwings low-cost airline unit, as the health crisis dents travel demand.
Lufthansa's shares jumped 8.1pc as another report said the company was working on a package to raise money from the debt and equity markets.
Cineworld, which has lost about three quarters of its value this year, surged 35.8pc after saying it was in talks lenders for its liquidity needs as the strict stay-at-home orders forced it to shut all its 787 cinemas across 10 countries.