A jump in Chinese factory activity despite the virus-hit global economy helped keep equities markets bubbling higher, but oil prices failed to rebound convincingly from 18-year lows.
Asia stocks picked up the baton from a rally Monday that saw all three of Wall Street's main indices jump more than three percent.
That carried over into Europe and back to New York, although gains were more modest.
"The release of Chinese PMI data overnight provided some reason for optimism, with a sharp rebound back into expansion lifting spirits ahead of the European session," said market analyst Josh Mahony at online trading firm IG.
China's manufacturing sector saw surprise growth in March, having been mauled in February as the country went into lockdown to tackle the virus.
China's Purchasing Managers' Index, a key gauge of factory activity, jumped to 52.0 from a record low 35.7 the month before. Any figure above 50 is considered growth.
China is slowly returning to a semblance of normal life after months of tough restrictions that confined millions of people at home and brought economic activity to a near standstill.
"Chinese factory data overnight gave a flicker of hope that the world's second largest economy is firing back up, despite large parts of the world grinding to a halt," said City Index analyst Fiona Cincotta.
The Chinese data initially helped oil prices rebound from 18-year lows struck on Monday as measures to contain the coronavirus outbreak have hit demand.
A strong and quick recovery of Chinese output would help boost demand for energy.
But European benchmark Brent crude began to fall once again, although the main US contract, WTI, was still up over two percent.
An ongoing price war between Russia and Saudi Arabia has also put downward pressure on prices.
"Until markets can start to understand how bad the demand shock will be since practically the whole world is on lockdown, most oil rallies will get faded," said analyst Edward Moya at OANDA.
'Bear market rally'
While the number of infections and deaths continues to rise, some observers believe traders are getting used to the new normal, with some suggesting the worst of the stock selloffs are over.
Trillions of dollars pledged to offset the economic impact of the deadly virus have provided a semblance of stability to world markets, which were initially pummeled by the rapid spread of the disease, which has forced swathes of the planet -- and the global economy -- into lockdown.
But others are more sceptical.
"It is becoming obvious that lockdown measures around the world will need to be extended, and that will likely make everyone’s GDP decline forecast a little uglier," said OANDA's Moya.
"Despite today’s stock market resilience, this is still probably a bear market rally," he added.
- Key figures around 1530 GMT -
London - FTSE 100: FTSE 100: UP 2.0 percent at 5,671.96 (close)
Frankfurt - DAX 30: UP 1.2 percent at 9,935.85 (close)
Paris - CAC 40: UP 0.4 percent at 4,396.12 (close)
Milan - FTSE MIB: UP 1.1 percent at 17,050.94 (close)
Madrid - IBEX 35: UP 1.9 percent at 6,785.40 (close)
EURO STOXX 50: UP 0.2 percent at 2,770.73
New York - Dow: UP 0.5 percent at 22,434.64
Tokyo - Nikkei 225: DOWN 0.9 percent at 18,917.01 (close)
Hong Kong - Hang Seng: UP 1.9 percent at 23,603.48 (close)
Shanghai - Composite: UP 0.1 percent at 2,750.30 (close)
Brent North Sea crude: DOWN 0.5 percent at $22.64 per barrel
West Texas Intermediate: UP 2.2 percent at $20.53 per barrel
Euro/dollar: DOWN at $1.1006 from $1.1046 at 2230 GMT
Dollar/yen: DOWN at 107.63 yen from 107.72
Pound/dollar: DOWN at $1.2447 from $1.2406
Euro/pound: DOWN at 88.40 pence from 89.07 pence