Stock prices in South Korea, the Philippines and Indonesia jumped by more than six percent, and key indexes in Australia and Hong Kong rallied more than three percent.
The recovery in Australian stocks, which went into freefall at the end of last week, followed a decision by the government to spend more than $7 billion to try to stave off recession.
The funds will come from the budget surplus, which has been amassed largely on the back of a mining boom that has seen vast quantities of Australian minerals exported to China and India.
Some economists say the stimulus package may not be enough to prevent Australia slipping into a recession after 17 years of uninterrupted growth.
In a nationwide address, Australian Prime Minister Kevin Rudd was optimistic about the future, but said that immediate action was needed.
"The global financial crisis has entered into a new, dangerous and damaging phase, one which goes to the real economy, growth and jobs," said Mr. Rudd. "And that is why the government has decided to act decisively and early on the question of this economic security strategy for the future; an economic security strategy to help underpin positive economic growth into the future and to provide practical support for households."
The recovery of Asian stock markets followed a surge in the Dow Jones Industrial Average, which gained more than 11 percent Monday - its biggest one-day gain since 1933.
Investors were reacting to efforts by the U.S. government to inject capital into banking system to stimulate lending, which has dried up in the global credit meltdown.