European share indexes initially shot up, but then fell back again, after the US central bank slashed its key interest rate to 3.5% from 4.25%.
US shares have opened sharply lower despite the US central bank's shock decision to cut interest rates to 3.5% from 4.25%.
London's FTSE 100 index rose 1.9% on the move, but lost the gains quickly to fall 0.3%. Frankfurt's Dax fell 2.3% and in Paris, the Cac 40 slid 1.3%.
The Dow Jones Industrial Average fell 3.7% in early trading while the technology-based Nasdaq fell 5.0%.
The rate cut came after global stocks had tumbled on Monday, posting their worst day since the 9/11 attacks.
European share indexes initially shot up, but then fell back again, with the FTSE down 0.3%, the Dax down 2.3% and the Cac 40 in Paris down 1.2%.
Some analysts are concerned that the rate cut was a sign of panic.
There is concern that the dramatic rate cut may be seen as a sign of panic.
"The Fed is very, very, very worried," said John Tierney at Deutsche Bank.
"If it looks like panic at the Fed, smells like panic at the Fed, and quacks like panic at the Fed, well many will say it is panic at the Fed," said BBC business editor Robert Peston.
"For now, it's going to put a floor on the market."
Before the rate cut, US index futures had suggested that New York share markets were likely to fall by as much as 5% when they opened just before 1430 GMT.
Earlier, Asian markets had tumbled with Japan's Nikkei 225 index closing down 5.7%, taking its decline this year to 18%.
'Scary and grizzly'
Many analysts are predicting indexes will remain volatile in coming weeks.
"I think we can safely say that the stomping, snorting optimistic beast of a market is fleeing the field, to be replaced by something scary and grizzly," said BBC Business Editor Robert Peston.
HAVE YOUR SAY Markets will recover again as they always do. In the meantime we have to tighten our belts! Richard, London Send us your comments
"But volatility is the order of the day. In London, there has been a stunning bounce, which could yet turn out to be ephemeral.
"Having worked at assorted times on trading floors, I can smell the adrenalin, testosterone and fear that is creating this mayhem," he said.
The recent falls were triggered by fears of a global recession. Concern had been growing that a proposed US stimulus package, involving about $145bn (£76bn) in tax cuts to encourage spending, might not be enough.
Dominique Strauss-Kahn, the head of the International Monetary Fund, said the global economic situation was "serious" and that all countries in the world were suffering in the wake of a slowdown in US growth.
British Prime Minister Gordon Brown said the UK was well-placed to weather the storm.
He promised that the government would do "everything in its power to maintain economic stability".
