"Meanwhile, the Italian lockdown raises fears of similar action for other European nations." In late morning trade, London's benchmark FTSE 100 index of major blue-chip companies was up 4.0 per cent, aided by a 10-per cent rebound in oil prices despite the Saudi announcement.
In the eurozone, Frankfurt's DAX 30 jumped 3.5 per cent and the Paris CAC 40 rallied 4.2 per cent.
In Milan, the FTSE MIB won 3.3 per cent after plunging more than 11 per cent Monday, as the Italian government unveiled more drastic measures to curb the coronavirus outbreak there.
"Europe is off to a more positive start on Tuesday, after stocks suffered their worst losses since the global financial crisis at the start of the week," said analyst Craig Erlam at traders OANDA.
"On any ordinary day, gains of a couple of percent in indices would be a solid day but given the scale of yesterday's decline, it could well be nothing more than a dead cat bounce." Investors often express scepticism about a recovery that follows a heavy fall in a stock or market by referencing the idea that even a dead cat will bounce if it falls from a great enough height.
On Monday, both London and Paris suffered their biggest daily drops since the 2008 global financial crisis -- while Frankfurt experienced its sharpest single fall since 2001.
Analysts however remained sceptical that the gains would hold as the global coronavirus crisis shows no sign of abating.
Italy is the most affected country after China and overnight the government announced the entire country would be locked down because of the fatal COVID-19 outbreak.
Global stock markets had collapsed on what has become known as "Black Monday", with the Dow on Wall Street plunging more than 2,000 points, triggering an emergency break in trade.
Asia had suffered a meltdown as the deadly virus continues to infect thousands. But there was relief on Tuesday as oil jumped more than eight percent after plunging by a third the previous day, in the worst session since the 1991 Gulf War.
The rush for safe investments also sent yields on US Treasuries to record lows, while the VIX "fear" index is within touching distance of its record high seen during the global financial crisis.
After a shaky start that had sparked fears of another rout, Asia equities pushed into positive territory, with energy firms clawing back some of their massive losses.
Gulf stocks also saw a bounce, with markets in Saudi Arabia and Dubai both up more than five percent, Abu Dhabi gaining 4.2 percent, and Kuwait and Qatar also making big advances.
But Russia's RTS stock index dived more than 10 percent in early trading. Sentiment was boosted by news that Chinese President Xi Jinping had visited Wuhan, the centre of the virus outbreak, lifting hopes that the country is well on track to recovery as new infections fall.
The news comes after weeks of quarantines that have rocked the global and local economy.
While the outbreak appears to be slowing in China, investors are desperately looking for signs of an easing in Europe and the United States.
Italy is now the worst-hit country outside China, with more than 9,000 cases and hundreds of deaths. On Monday, Prime Minister Giuseppe Conte said he was extending restrictions on travel and public gatherings initially imposed on the north to the entire country.
Speculation is also mounting that the Federal Reserve will cut interest rates again, having slashed them unexpectedly last week.
Trump said his administration would be meeting lawmakers to discuss economic relief measures to mitigate the impact of the disease as it spreads through the United States.
The spread of COVID-19 is putting a huge strain on economies and stoking concerns of a worldwide recession.
The crisis has now been compounded by an oil price war between Saudi Arabia and Russia that sparked Monday's crude price plunge.
Benchmark oil contract WTI rebounded by more than ten percent on Tuesday, but remained at an ultra-low level after diving by around a quarter a day earlier.
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