"Equities appear to offer value at current levels, they are clearly oversold in the short-term and policy-makers are, somewhat belatedly, taking action to support the system and the economy," said Tony Dolphin, director of economics and asset allocation at Henderson Global Investors.
By early-afternoon London time, Germany's DAX was 76.14 points, or 1.5 percent, higher at 5,,077.30, while France's CAC-40 was up 88.63 points, or 2.5 percent, at 3,585.52. The FTSE 100 index of leading British shares was 59.59, or 1.4 percent, higher at 4,426.28.
All three indexes had been around 3 percent higher earlier in the session, but some profit-taking ahead of the bell in New York appeared to prompt the modest retreat.
Nevertheless, Wall Street appears to be heading for a strong open after IBM Corp. reaffirmed its profit outlook and investors hoped that the panic selling that cascaded through global markets a day earlier was over, at least for now. Dow futures rose 136, or 1.46 percent, to 9,327.
Britain's benchmark index was helped higher by a positive reaction to the British government's rescue package, with shares in the two most troubled banking stocks gaining plenty of ground. HBOS PLC stock was up 30 percent, while Royal Bank of Scotland added 13 percent.
The British goverment pledged some 50 billion pounds to buy stakes in the country's major banks, as well as underpinning bank finances by a further 450 billion pounds (US$778 billion).
It wasn't just British banking stocks doing well today. In Germany, Hypo Real Estate Holding AG, which has received a government-sponsored rescue, was up more than 12 percent, Commerzbank AG bounced more than 9 percent and Deutsche Bank AG was nearly 6 percent higher.
And the news that the governments of France, Belgium and Luxembourg will give struggling lender Dexia SA a yearlong guarantee on its new loans and deposits, sent the company's shares soaring by 18 percent.
No one in the markets though is willing to call an end to the turmoil that has gripped stock markets over the last few days, until banks start lending to each other and money market rates decline and spreads narrow.
The pressures will remain for some time, according to U.S. Treasury Secretary Hank Paulson, who warned that further banks in the world's largest economy will fail despite the US$700 billion bailout package agreed by U.S. lawmakers just last week.
The nationalization of Kaupthing, Iceland's largest bank, has also fueled concerns about the viability of the financial sector in Europe.
Britain's bailout has stoked talk that the U.S. will do something similar to stabilise its banking system.
Asked whether he would try something like the British plan, Paulson told reporters Wednesday that the U.S. Treasury has "a broad range of authorities and tools. ... We've emphasized the purchase of liquid assets, but we have a broad range of authorities. And I'm confident we have the authorities we need to work with going forward."
However, some analysts are not sure that the Emergency Economic Stabilization Act does give Paulson that authority.
"Even if the US Treasury were to utilize the whole US$700 billion provided for in the TARP in directly supporting US financial institutions, it would not stretch very far," said Stephen Lewis, an analyst at Monument Securities in London, using the acronym applied to the U.S. bailout when it was first introduced.
Asian markets were mixed overnight as investor enthusiasm over Wednesday's rate cuts around the world was tempered by ongoing fears about the strains in the credit markets and the prospect of a deep global recession, which would hit Asian exporters hard.
South Korea, Hong Kong and Taiwan followed the lead of the world's leading central banks and lowered their interest rates too.
Tokyo's benchmark Nikkei 225 index rose more than 1 percent but fell back to close down 0.5 percent to 9,157.49, a five-year low. That followed a 9.4 percent plunge Wednesday, its biggest one-day drop since the 1987 market crash.
Hong Kong's Hang Seng index gained 3.6 percent to 15,985.39, while South Korea's key index rose 0.6 percent after earlier rising as much as 2.9 percent.
Mainland China's main index fell 0.8 percent as investors continued to unload shares in banks and property firms even after its central bank lowered rates Wednesday.
In Indonesia, trading on the Jakarta Stock Exchange was canceled Thursday after the benchmark JSX index sank 10.4 percent Wednesday before trading was suspended by late morning. Authorities ordered the market to stay closed, possibly through Friday, following a late night Cabinet meeting.
Associated Press business writer Elaine Kurtenbach in Shanghai and writers Shino Yuasa in Tokyo and Kelly Olsen in Seoul contributed to this report.