Investors fear that efforts to halt the banking crisis won't prevent recession
Wall Street shares ended higher after sharp falls and gains in a day of tense trading, with the Dow closing up 4.6%.
Yahoo shares jumped on talk of a deal with Microsoft and pushed the Nasdaq index up 5.4%.
Investors were digesting September's industrial production figures - which made their biggest drop since 1974 - while inflation was unchanged.
In Europe, London's FTSE 100 closed down 5.7%, France's Cac 40 fell 5.9% and Germany's Dax lost 4.9%.
The Dow Jones Industrial Average closed at 8,979 after a late rally, while the technology-based Nasdaq index ended the day at 1,717.
Wall Street is expected to remain extremely volatile, as it has been since last month, because of investors' great anxiety about the economy.
"We're going to continue to see volatility. You're not going to see 50-point ranges, you're going to see two-three-four hundred point ranges," said Woody Dorsey, of the financial forecasters Market Semiotics.
Tom Higgins of Payden & Rygel investment managers said some investors were being forced to use the stock market because other markets remained largely paralysed.
"If you have to liquefy your assets and you need access to cash immediately then the market you're going to do it in is the equity market and that's what I think is pushing around the indexes," he said.
On Wednesday, the Dow recorded its biggest one-day percentage fall since October 1987, closing almost 8% down.
DOW JONES INDUSTRIAL AVERAGE: 16 October 2008
*All Times GMT
Other developments included:
US industrial production fell 2.8% in September, figures showed
US consumer price inflation was unchanged in September from August
The Philadelphia Federal Reserve's report showed manufacturing conditions had weakened in October
Oil prices fell after weekly US fuel reserves figures rose more than expected; US light, sweet crude for November delivery hit a 14-month low of $69.93 a barrel
Germany lowered its forecast for economic growth next year from 1.2% to 0.2%
FTSE 100 INDEX: 16 October 2008
*All Times GMT
The US inflation figures were better than had been expected, despite the low interest rate policy being pursued by the central bank, the Federal Reserve.
Hurricanes in the Gulf of Mexico and a strike at Boeing were partly blamed for the big fall in industrial production, which hit sentiment.
"It is one for the record books, or just about," said Chris Rupkey at Bank of Tokyo-Mitsubishi UFJ in New York.
"It is a sign that the economy is falling away quickly, and it is certainly consistent with the recession that we seem to be in."
Shares rose earlier in the week on optimism after more details emerged about the bank rescue packages being proposed by the UK and the European Union.
What we're witnessing is the limits of what these banking bail-outs can achieve in the face of what increasingly looks like the onset of a global economic recession
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.