The Dow Jones index of leading U.S. shares was 183.19 points, or 2.0 percent, higher, having opened nearly 400 points higher.
In London, the FTSE 100 index of leading shares was up 146.94 points, or 3.5 percent, at 4,403.84 by late afternoon local time despite news that inflation in Britain is running at a 16-year high. Germany's DAX was up 167.54, or 3.3 percent, at 5,229.99 even though a group of leading German economic think tanks said Tuesday that Europe's largest economy is on the "brink of a recession."
The CAC-40 in France was 151.95 points, or 4.3 percent, stronger at 3,683.45.
The resurgence in the markets follows unprecedented government efforts to bring an end to the financial crisis that has threatened the outlook for the whole global economy.
So far, government actions appear to have worked, at least in terms of boosting confidence in the financial markets.
"The sense of relief is obviously pulpable, in terms of the share price gains, but minds will soon turn back to the state of the global economy," said Richard Hunter, a strategist at Hargreaves Lansdown in London.
The U.S. became the latest to announce plans buy stakes in its banks.
President George W. Bush unveiled the $250 billion plan to buy stakes in nine banks and argued that the drastic steps would help stability return to the U.S. banking sector. "This is an essential short-term measure to ensure the viability of America's banking system," Bush said.
The U.S. package comes a day after European governments, unveiled plans to take stakes in their banks under a package of guarantees and other emergency measures worth some euro1.7 trillion ($2.3 trillion).
The long-term key to whether the rescue packages work is whether the flurry of activity can actually break the logjam in credit markets and the early indications are that there has been some easing in rates and spreads.
The interbank lending rate for three-month euro loans, known as the Euro Interbank Offered Rate, or Euribor, fell 0.08 percentage points to 5.24 percent from 5.32 percent the day before. Rates had fallen on Monday as well, but by a more modest 0.06 percentage points.
The equivalent dollar rate fell 0.12 percent to 4.64 percent, while pound rates are 0.02 percent down at 6.25 percent.
Though the rates are falling, the differential between the rate at which banks lend to each other and official central bank lending rates remain high, signalling a strong degree of mistrust still exists. In the U.S. the base central bank rate is 1.5 percent, in the euro area it is 3.75 percent and 4.50 percent in Britain.
"The money markets remain the focus to gauge the extent to which healing has occurred and the conclusion is that these are early days," said Divyang Shah, a strategist at Commonwealth Bank of Australia.
Earlier, Asian governments took more steps to fortify their own financial systems, helping stock markets across the region to rally. Authorities relaxed regulations on companies buying up their own shares, a change that will help prevent takeovers and allow companies to prevent a nose-dive in their own issues.
Japan also promised to continue to protect people's insurance policies and savings accounts, and said it will consider capital injection into medium-size and small Japanese financial institutions.
And in Australia, the government announced a plan to inject 10.4 billion Australian dollars ($7.4 billion) to strengthen the country's economy, helping send the S&P/ASX200 index 3.7 percent higher. Hong Kong promised to guarantee all bank deposits until 2010.
Hong Kong's key index ended up 3.2 percent, while South Korea's market jumped over 6 percent. The Philippine market surged more than 7 percent and Indonesia's market - shut half of last week due to dramatic declines - was up more than 6 percent.
Only China's market fell - sliding 2.7 percent.
Russia's stock markets joined the surge Tuesday, prompting regulators to suspend trading on one of the two major exchanges.
The MICEX, where most of Russia's trading takes place, climbed 11.2 percent before trading was halted for an hour. The RTS climbed 6.4 percent.
Oil continued to rise, with light sweet crude for November delivery gaining $0.76 to $81.95 a barrel in European trade on the New York Mercantile Exchange.
In currencies, the dollar was slightly lower on the day at 102.65 yen, and the euro was stronger at $1.3715, though off earlier highs.
