The Nikkei surged after a dismal performance last week
Financial markets in Asia have risen sharply, with Japan's Nikkei index gaining a record 14%.
The gains came after Wall Street shares rocketed 11% on Monday as investors welcomed fresh moves to deal with the worldwide financial crisis.
Investors were helped by news the US government wanted to put in place its $700bn (£400m) bank bail-out quickly.
Australian Prime Minister Kevin Rudd has now announced a A$10.4bn ($7.3bn) economic stimulus package.
It will allow for one-off payments to the country's low-wage earners and pensioners and follows earlier announcements of guarantees of bank deposits for three years.
According to Mr Rudd, the strategy "will strengthen the national economy and support Australian households".
Australia's main share index ended the day up 3.7%.
Australian PM Kevin Rudd announces a A$10.4bn economic stimulus package
In Japan, the Nikkei 225 stock average soared 1,171.14 points, or 14.15% at 9,447.57 - its biggest ever percentage gain.
The Japanese stock exchange was closed on Monday.
In Hong Kong, the Hang Seng index was up 715.67 points, or 4.4%, at 17,027.83 by the mid-session break. South Korea's index finished the day 6.14% higher.
In the US, President George W Bush is due to make a statement shortly before markets open there later on Tuesday.
He will speak after meeting his working group on financial markets.
Rescue plans
On Monday, US Treasury and Federal Reserve Bank officials met the chief executives of some of America's biggest banks, to work out details of the US government's $700bn bail-out package.
It seems Mr Brown and Co. have no choice in this matter and these takeovers are necessary, but its very wrong that it is the tax payer that should have to do this
The US Treasury also announced it was set to buy stakes in a "broad array" of financial firms.
Treasury Secretary Henry Paulson will give further details of the plan on Tuesday morning, with an expectation that funds will be injected into such major banks as JP Morgan Chase, Goldman Sachs and the Bank of New York Mellon Corp.
European governments have said they are putting up to 1.7 trillion euros ($2.3 trillion; £1.3 trillion) to protect the continent's banks through guarantees and other emergency measures.
The sums are a maximum, and might not all be spent if the financial crisis eases.
So far Germany has approved a bank rescue plan worth up to 500bn euros, France will spend about 350bn euros, the Netherlands has pledged 200bn euros, Spain 100bn euros, and Austria 85bn euros.
Italy said it would spend as much as was needed, without giving any exact figures.
The bulk of the European money will be used to guarantee lending between banks - part of a plan agreed this weekend by the 15 nations that use the euro.
The cash will also be used to take stakes in ailing banks, with the UK government saying it would inject up to £37bn of taxpayers cash into Royal Bank of Scotland, Lloyds TSB and HBOS.
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